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Rock shed is an effective protection measure against rockfall. To investigate the influences of falling rock’s shape and impact angle on the impact effect of the cushioned rock shed, a modeling approach for a rock shed with a cushion layer using PFC-FLAC. The granular cushion is modeled as an aggregate of discrete non-cohesion particles, while the concrete plate and the beam are modeled as zones. The falling rock with different sphericities and impact angles is modeled as a rigid assembly. The numerical model is validated by comparing the simulation results with experimental and numerical results from previous literature. This model is applied to analyze the effects of rock shape and impact angle on the dynamic interaction effects between falling rock and cushioned rock shed, including the impact force, transmitted bottom force, penetration depth, and plate deflection. The numerical results show that the variation in the falling rock’s shape has different effects on the falling rock with different impact angles. These findings could support rock shed design by revealing the limitations of the assumptions in the past research, which may result in unsafe rock sheds for some rockfall cases.

Abrasive water jet is a highly efficient cutting technology. Through some sandstone cutting tests, the research on the optimal impact angle and inclined cutting mechanism of rock-like materials is carried out. Based on the macroscopic and microscopic observation of the cut’s inner wall, crystal glass cutting experiments are conducted to investigate the cutting motion process of abrasive water jet under different impact angles, revealing the variation laws of cutting depth, the characteristics of the cut’s inner wall, the trajectory of abrasive particles and the type of crystal destruction under different cutting pressures and impact angles. The test results show that the average cutting depth gradually increases with the increase of cutting pressure, while changing the impact angle can significantly change the jet’s cutting ability, and the best cutting effect is obtained at an impact angle of 75°. With the increase of the cut depth, the curved jet trajectory texture gradually appears in the cut’s inner wall , and in its bottom there are typical erosion pits and trailing phenomenon. The cut’s inner wall is mainly characterized by four types of damage features such as fracture through the crystal, fracture along the crystal, cut grooves or pits, and cement coverage, etc. It is worth noting that the four types of damage features appear at different locations in the cut at different impact angles, and this phenomenon is mainly caused by the deflection of jet, the direction of reflected flow movement, and the change in the reflection of shock wave and expansion wave. The vertical and horizontal jet components (in the same direction as the direction of propulsion), which play a dominant role in the destruction of the target, and the horizontal jet component, which is opposite to the direction of propulsion, play a secondary role in the erosion and polishing of the formed cut, but the degree of action varies under different impact angles. The macroscopic model of the abrasive water jet cutting process is established by combining the trajectory texture of cut’s inner wall and the observation results of the jet cutting process. The research results can provide a technical reference for further improving the efficiency of abrasive water jet cutting.

In planetary surfaces, oblique impact events are commonplace, and their study holds significant importance for understanding planetary impact processes and aiding in the design of landers and impactors. Current research predominantly focuses on simplified models to study the force and motion under vertical impact craters in terms of scale and impact loading. For oblique impacts, investigations have primarily concentrated on the final crater shape. However, the specific influence of impact load motion on particle bed movement and the precise impact angle’s effect on the ultimate crater shape during the impact process remain unclear. In this study, we used a custom-built oblique impact experimental setup to analyze changes in the velocity field of the particle bed and the horizontal movement of the impact load. Using quasi-static region to assess ellipticity, we aimed to reveal the state of particle movement during oblique impacts and explore the impact of impact angles and energies on crater formation. The results indicate that under large impact angles, the obliquely acquired kinetic energy is minimal, leading to a predominant static point source movement of the particle bed. At higher energy levels, the impact load primarily excavates downward, resulting in the formation of circular impact craters. These findings underscore the sensitivity of particle bed motion to impact angles, making it a crucial metric for assessing the impact of oblique angles on final crater morphology.

In order to investigate the effect of the carrier's initial velocity on the jet's damage power, this paper conducted the numerical simulation of a jet penetrating thick‐walled targets at various following velocities (the carrier's initial velocity). For large stand‐off distance (D), the influence on jet formation parameters was revealed under different following velocities (ranging from 0 to 1000 m/s), and the jet's penetration performances were analyzed at various stand‐off distances (ranging from 3D to 10D). Then, taking 3D as an example, the study investigated the influence mechanism of the coupling between following velocity and impact angle (ranging from −60° to 60°) on jet penetration performance. The results show that an increase in the following velocity causes the jet to bend and break at an earlier time. The following velocity has a minimal effect on jet tip velocity. Additionally, the lateral displacement is linearly correlated with stand‐off distance. For normal penetration, the jet penetration depth decreases exponentially as the following velocity increases at the same stand‐off distance. Especially, the penetration depth decreases by over 80% when the following velocity exceeds 600 m/s, and a further increase in the following velocity has a minimal effect on jet penetration depth. A greater jet penetration depth was achieved for the climbing‐oblique penetration (COP) than the diving‐oblique penetration (DOP) due to an increase in dynamic stand‐off distance. Finally, the ratio of oblique to normal penetration depth for a jet with varying following velocities was derived based on the theory of steady‐jet and hole expansion, and its accuracy was verified. [ABSTRACT FROM AUTHOR]

The simultaneous oblique impact of multiple droplets on a liquid film is an intricate phenomenon prevalent in diverse natural and industrial processes. However, previous studies have primarily focused on single droplet impact, while an in-depth understanding of the more complex multi-droplet scenario remains lacking. The current study aims to numerically investigate the simultaneous oblique impact of two droplets on a water film using a three-dimensional Volume of Fluid (VOF) model. The effects of the Weber number and the impact angle on the crown behavior are carefully analyzed. The results demonstrate that increasing the Weber number enhances the central uprising sheet height but has minor influences on the upstream crown radius and central sheet radius. In contrast, the increase in the impact angle leads to a decreased upstream crown radius and an increased central sheet radius, while the central sheet height remains relatively unaffected. In addition, the splashing threshold for the dual droplet impact cases is significantly lower than that of the single droplet impact cases due to the interactions between the adjacent crowns. The present results provide novel insights into the underlying physics and useful supports in developing predictive models for the intricate multi-droplet impact phenomenon. [ABSTRACT FROM AUTHOR]

For flood discharge structures with high water heads, aeration facilities are usually installed in engineering to promote water flow aeration and prevent cavitation damage to the overflow surface. Actual engineering has shown that as the slope of the discharge channel bottom decreases or water level changes lead to a decrease in the Froude number, the cavity morphology after conventional aeration facilities or allotype aerators is poor. This article proposes a curved aeration facility scheme based on the idea of locally increasing the bottom slope to reduce the impact angle, which is formed by the convex parabolic bottom plate and concave parabolic bottom plate. The convex parabolic bottom plate is tangent to a flat bottom plate behind the offset, and the concave parabolic bottom plate is tangent to the downstream. The jet landing point is controlled at the junction of the convex parabolic bottom plate and the concave parabolic bottom plate, and the lower jet trajectory is in line with the parabolic bottom plate. The corresponding parabolic bottom plate calculation formulas were theoretically derived, and the design method of the shape parameters of the aeration facility was provided. Through specific engineering case studies, it was found that: (1) As the ZAC/ZAG value increases, point C becomes closer to point G, the slope of the water tongue landing point C becomes steeper, and the cavity is less likely to return water. (2) When the position of the water tongue landing point is 0.5–0.8 times the height of the water tongue impact point, there is almost no water accumulation in the calculated cavity. At this time, the platform length LAB = 0.5LAF, the convex parabolic section length LBC = (0.45–0.6) LAG, the concave parabolic section length LCD = (0.43–0.11) LAG, the convex parabolic section calculation formula is z (x) = −A1x2 (A1 = 0.0059–0.00564), and the concave parabolic section calculation formula is A2x2 − B2x2 (A2 = 0.003347–0.01927).This solved the problem of aeration and corrosion reduction under small bottom slope, large-unit discharge, and low Froude number engineering conditions. [ABSTRACT FROM AUTHOR]

In order to study the deformation and failure law of bolt-mesh support roadway under roof impact load, taking 250104 transport roadway of Huating Coal Mine as background, FLAC3D was used to analyze the variation characteristics of stress, deformation and plastic zone of surrounding rock of bolt-mesh support roadway under different impact load wave velocities, angles and offset distances. The results show that: under the impact of roof load, the plastic zone of roadway roof and rock mass on both sides will gradually expand to upward and both sides, and its maximum displacement will increase exponentially; with the increase of the wave velocity of the roof impact load, the maximum displacement of the roadway roof and two sides will gradually increases exponentially; with the increase of impact angle of roof impact load, the maximum displacement of the roadway roof and two sides presents an “S-shaped” growth curve, and the impact angle of 90° has the most adverse impact on the stability of the surrounding rock of the roadway with bolt-mesh support; with the increase of the impact offset distance of roof impact load, the maximum displacement of roadway roof and impact side rock will increase first and then decrease. When the impact offset distances is equal to 5.0 m, it will pose the greatest threat to roadway safety.

Erosion is a phenomenon and is the primary cause of failure in numerous slurry transportation equipment such as pump impellers, pipeline fittings, etc. It reduces the working life of the equipment and is thus an essential factor in the design, choice, and operation of any system. Pipeline materials used to convey slurry often experience severe wear from erosive forces. Researchers are interested in minimizing erosion wear using different coatings to increase equipment life. The High-Velocity Oxy-Fuel (HVOF) spray technique was employed to deposit WC-10Co-4cr + 2% TiO2 coating on the SS409. The erosion wear was evaluated using a slurry jet erosion tester of uncoated and coated materials with sand as the erodent. The impact of impingement angle, velocity, time, and other parameters was studied. On the erosion wear of uncoated and coated materials, it was found that the influence of jet velocity was greater than the impact of other parameters. The deteriorated surfaces were analyzed using a scanning electron microscope (SEM). The erosion wear resistance of SS 409 was significantly improved by the WC-10Co-4cr + 2% TiO2 coating. The coating demonstrated a brittle mechanism of erosion wear. Furthermore, image processing software investigated the mechanism of erosion wear.

The development of high wear/erosion resistance materials for defense application is found to be a challenging task among the researchers. The current study investigated the reinforcement effect of TiC and Rice husk ash (RHA) on Al6061 hybrid composites made using a two-step ultrasonic-assisted stir casting process. Four distinct Al6061 hybrid composites were created with varying TiC weight percentages (3, 6, 9, and 12 wt.%). RHA weight percentage was kept constant at 3%. The solid particle erosion test was carried out on each composite using a Taguchi L27 (33) orthogonal array. Experiments were conducted by varying the erodent particle impact angle, erodent velocity, and erodent discharge rate. The effect of each parameter on the erosion rate of the TiC/RHA Al6061 composite was discussed. The composite containing 12% TiC and 3% RHA showed improved erosion resistance. It was found that on increasing the TiC addition in the composite resulted in an increase in erosion resistance. SEM images were used to examine the surface failure on the composites caused by erodent impact.

Polyurethane is widely used on the surface of composite materials for rotor blades as sand erosion protection materials. The failure mechanism investigation of polyurethane film under service conditions is useful for developing the optimal polyurethane film for rotor blades. In this article, the sand erosion test parameters were ascertained according to the service environment of the polyurethane film. The sand erosion resistance and failure mechanism of polyurethane film at different impact angles were analyzed by an infrared thermometer, a Fourier transform infrared spectrometer (FTIR), a differential scanning calorimeter (DSC), a field emission scanning electron microscope (FESEM), and a laser confocal microscope (CLSM). The results show that the direct measurement method of volume loss can better characterize the sand erosion resistance of the polyurethane film compared to traditional mass loss methods, which avoids the influence of sand particles embedded in the polyurethane film. The sand erosion resistance of polyurethane film at low-angle impact is much lower than that at high-angle impact. At an impact rate of 220 m/s, the volume loss after sand erosion for 15 min at the impact angle of 30° is 57.8 mm3, while that at the impact angle of 90° is only 2.6 mm3. The volume loss prediction equation was established according to the experimental data. During low-angle erosion, the polyurethane film damage is mainly caused by sand cutting, which leads to wrinkling and accumulation of surface materials, a rapid increase in roughness, and the generation of long cracks. The linking of developing cracks would lead to large-scale shedding of polyurethane film. During high-angle erosion, the polyurethane film damage is mainly caused by impact. The connection of small cracks caused by impact leads to the shedding of small pieces of polyurethane, while the change in the roughness of the film is not as significant as that during low-angle erosion. The disordered arrangement of the soft and hard blocks becomes locally ordered under the action of impact and cutting loads. Then, the disordered state is restored after the erosion test finishes. The erosion of sand particles leads to an increase in the temperature of the erosion zone of the polyurethane film, and the maximum temperature rise is 6 °C, which does not result in a significant change in the molecular structure of the polyurethane film. The erosion failure mechanism is cracking caused by sand cutting and impact. [ABSTRACT FROM AUTHOR]

The simultaneous oblique impact of multiple droplets on a liquid film is an intricate phenomenon prevalent in diverse natural and industrial processes. However, previous studies have primarily focused on single droplet impact, while an in-depth understanding of the more complex multi-droplet scenario remains lacking. The current study aims to numerically investigate the simultaneous oblique impact of two droplets on a water film using a three-dimensional Volume of Fluid (VOF) model. The effects of the Weber number and the impact angle on the crown behavior are carefully analyzed. The results demonstrate that increasing the Weber number enhances the central uprising sheet height but has minor influences on the upstream crown radius and central sheet radius. In contrast, the increase in the impact angle leads to a decreased upstream crown radius and an increased central sheet radius, while the central sheet height remains relatively unaffected. In addition, the splashing threshold for the dual droplet impact cases is significantly lower than that of the single droplet impact cases due to the interactions between the adjacent crowns. The present results provide novel insights into the underlying physics and useful supports in developing predictive models for the intricate multi-droplet impact phenomenon.

For flood discharge structures with high water heads, aeration facilities are usually installed in engineering to promote water flow aeration and prevent cavitation damage to the overflow surface. Actual engineering has shown that as the slope of the discharge channel bottom decreases or water level changes lead to a decrease in the Froude number, the cavity morphology after conventional aeration facilities or allotype aerators is poor. This article proposes a curved aeration facility scheme based on the idea of locally increasing the bottom slope to reduce the impact angle, which is formed by the convex parabolic bottom plate and concave parabolic bottom plate. The convex parabolic bottom plate is tangent to a flat bottom plate behind the offset, and the concave parabolic bottom plate is tangent to the downstream. The jet landing point is controlled at the junction of the convex parabolic bottom plate and the concave parabolic bottom plate, and the lower jet trajectory is in line with the parabolic bottom plate. The corresponding parabolic bottom plate calculation formulas were theoretically derived, and the design method of the shape parameters of the aeration facility was provided. Through specific engineering case studies, it was found that: (1) As the ZAC/ZAG value increases, point C becomes closer to point G, the slope of the water tongue landing point C becomes steeper, and the cavity is less likely to return water. (2) When the position of the water tongue landing point is 0.5–0.8 times the height of the water tongue impact point, there is almost no water accumulation in the calculated cavity. At this time, the platform length LAB = 0.5LAF, the convex parabolic section length LBC = (0.45–0.6) LAG, the concave parabolic section length LCD = (0.43–0.11) LAG, the convex parabolic section calculation formula is z (x) = −A1x2 (A1 = 0.0059–0.00564), and the concave parabolic section calculation formula is A2x2 − B2x2 (A2 = 0.003347–0.01927).This solved the problem of aeration and corrosion reduction under small bottom slope, large-unit discharge, and low Froude number engineering conditions.

In this paper, based on terminal sliding mode control (TSMC), a cooperative impact time and angle constrained guidance (CITACG) law for multi-missile system with switching network topologies is proposed. The obtained CITACG is composed of two parts. One part is designed to make the missiles intercept the target from their predetermined impact angles. And the other part’s goal is to make the multiple missiles intercept the target simultaneously without predefining a common impact time. Sliding mode surface of the first part is designed based on TSMC, meanwhile integral terminal sliding mode control (ITSMC) and graph theory are applied to derive the second part of the CITACG. When the communication network switches between the connected topology and the disconnected one, a Lyapunov candidate function is introduced and the corresponding stability conditions are derived. The proposed guidance law is the summation of the two guidance parts, therefore it is a direct method and do not have to switch the guidance command between the impact angle constrained guidance law and the impact time constrained guidance law. The predetermined common impact time is not required in the proposed CITACG, and the missiles can automatically adjust themselves to intercept the target simultaneously by communicating between their neighbors. Numerical simulations demonstrate the great performance of the proposed guidance law. [ABSTRACT FROM AUTHOR]

In this paper, the research findings on erosion - corrosion of metal materials at home and abroad in recent years were mainly summarized, including research methods of erosion corrosion and external factors affecting erosion corrosion rate. At present, the research methods of erosion - corrosion were mainly carried out in the form of experimental method, supplemented by numerical simulation. The experimental methods primarily included the classification of experimental devices and the collection and characterization of experimental results. Besides, the influencing factors affecting the erosion corrosion rate were classified and compared. The main influencing factors included flow velocity, sand content, sand size， impact angle, liquid pH value, temperature, oxygen content, etc. In the future, the main developing directions of erosion - corrosion would be the following aspects: optimizing the structure of numerical model to predict the erosion - corrosion rate distribution diagram of materials and determining the weak areas of multiphase flow erosion - corrosion.

In this paper, a red-eared slider turtle is used as the prototype for the bionic design of the foamed silicone rubber sandwich structure. The effect of impact angle on the performance of the foamed silicone rubber sandwich structure against low-velocity impact is studied by the finite element method. The numerical model uses the intrinsic structure model of foamed silicone rubber with porosity and the three-dimensional Hashin fiberboard damage model. The validity of the model was verified after experimental comparison. Based on the finite element simulation of different impact angles and velocities, the relationship between impact velocity and residual velocity, as well as the penetration threshold at various impact angles are obtained, and the change law of impact resistance of foamed silicone rubber sandwich structure with impact angle and velocity, as well as the damage pattern of sandwich structure at different impact angles and velocities are given. The results can provide a basis for the impact resistance design of the bionic foamed silicone rubber sandwich structure. The results show that, at a certain impact speed, the smaller the impact angle, the longer the path of the falling hammer along the plane of the sandwich structure, the lighter the damage to the sandwich structure and the greater the absorbed energy, so that avoiding the impact from the frontal side of the sandwich structure can effectively reduce the damage of the sandwich structure. When the impact angle is greater than 75°, the difference in impact resistance performance is only 2.9% compared with 90°, and the impact angle has less influence on the impact resistance performance at this time. [ABSTRACT FROM AUTHOR]

Powder jet machining is a blast machining process in which micrometer-order particles are projected onto a workpiece at near-supersonic speeds, to remove the workpiece (abrasive jet machining (AJM)) or to deposit the particles (powder jet deposition (PJD)). We report a novel dental treatment method for powder jet machining using hydroxyapatite, which is the main component of teeth, as deposited particles. The surfaces and interdental spaces of human teeth are not only flat, but also have complex groove structures. However, PJD and AJM exhibit impact-angle-dependent machining phases. Therefore, it is necessary to investigate the effect of the particle impact angle on machining, before dental treatment. Furthermore, because machining interacts not only with the particle impact angle but also with the particle impact velocity, a comprehensive investigation of the effects of the machining parameters is required, for delineating the phase-transition conditions. Accordingly, in this study, we conducted machining experiments using hydroxyapatite particles (particle diameter, 2.16 μm) and four different blasting angles of 30°, 45°, 60°, and 90°, to infer the machining amount. Machining efficiency was evaluated based on the amount of machining. The impact angles and velocities of the particles were calculated using computational fluid dynamics (CFD). Three-dimensional process mapping was performed using the machining amount, particle impact angle, and particle impact velocity, obtained from the experiments and CFD calculations. The results showed that PJD crossed to AJM at the impact angle of approximately 60°. Moreover, PJD exhibited high processing efficiency for impact angles above 60° and impact velocities in the 280–310 m/s range. In contrast, AJM exhibited high processing efficiency for impact angles below approximately 35° and impact velocities above 310 m/s. [ABSTRACT FROM AUTHOR]

Polyurethane is widely used on the surface of composite materials for rotor blades as sand erosion protection materials. The failure mechanism investigation of polyurethane film under service conditions is useful for developing the optimal polyurethane film for rotor blades. In this article, the sand erosion test parameters were ascertained according to the service environment of the polyurethane film. The sand erosion resistance and failure mechanism of polyurethane film at different impact angles were analyzed by an infrared thermometer, a Fourier transform infrared spectrometer (FTIR), a differential scanning calorimeter (DSC), a field emission scanning electron microscope (FESEM), and a laser confocal microscope (CLSM). The results show that the direct measurement method of volume loss can better characterize the sand erosion resistance of the polyurethane film compared to traditional mass loss methods, which avoids the influence of sand particles embedded in the polyurethane film. The sand erosion resistance of polyurethane film at low-angle impact is much lower than that at high-angle impact. At an impact rate of 220 m/s, the volume loss after sand erosion for 15 min at the impact angle of 30° is 57.8 mm3, while that at the impact angle of 90° is only 2.6 mm3. The volume loss prediction equation was established according to the experimental data. During low-angle erosion, the polyurethane film damage is mainly caused by sand cutting, which leads to wrinkling and accumulation of surface materials, a rapid increase in roughness, and the generation of long cracks. The linking of developing cracks would lead to large-scale shedding of polyurethane film. During high-angle erosion, the polyurethane film damage is mainly caused by impact. The connection of small cracks caused by impact leads to the shedding of small pieces of polyurethane, while the change in the roughness of the film is not as significant as that during low-angle erosion. The disordered arrangement of the soft and hard blocks becomes locally ordered under the action of impact and cutting loads. Then, the disordered state is restored after the erosion test finishes. The erosion of sand particles leads to an increase in the temperature of the erosion zone of the polyurethane film, and the maximum temperature rise is 6 °C, which does not result in a significant change in the molecular structure of the polyurethane film. The erosion failure mechanism is cracking caused by sand cutting and impact.

In this article, we investigate a cooperative guidance problem against a maneuvering target with impact angle coordination. As is well established, the main challenge is how to design a guidance law for each missile to intercept the target from specified directions with only the local information and information from its connected neighbors. Toward this, we prove that the underlying problem can be treated as a Nash equilibrium (NE) seeking problem, where each missile attempts to minimize its own performance index to achieve interception without unilaterally implicate the team objective, and then we introduce a local observer to facilitate the local implementation of the proposed guidance protocol by ensuring the seeking of NE distributive. Numerical simulations verified the performance of the proposed guidance strategy. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this research is to study the trend of pedestrian lower extremity injuries during vehicle-pedestrian collisions. Methods: In this study, pedestrian’s age, collision angle and pedestrian’s position are considered influencing factors. Nine experiments using a novel lower extremity mechanical model are designed with the orthogonal experiment method. Results: Under the same collision angle, collisions in the left and right positions caused more serious tibia injuries than the middle position. As for the collision angle, the tibial injury at +45° is more significant than the tibial injury at −45°, and the injury of oblique collisions is slightly greater than that at 0°. Moreover, tibial injury is more sensitive to research variables than femoral injury. When the collision angle and position are changed, the difference ratio of tibia stress is by 483.2% higher than that of femur stress. The axial force and bending moment of the quadriceps tendon in the left-position collision reach peak values, which are 3.83 kN and 165.98 Nm, respectively. The peak quadriceps tendon axial force is captured with the collision angle of −45°, and the peak quadriceps tendon bending moment is obtained with a collision angle of +45°. Conclusions: The effects of differences in impact position and angle on lower extremity injury in the elderly were analyzed, and the results of this study can be used as a reference for research on lower extremity protection. [ABSTRACT FROM AUTHOR]

Experiments of a single droplet oblique impact on a thin liquid film are carried out. In the experiments, the impact angle is adjusted by varying a horizontal airflow, and three typical initial droplet shapes of the sphere, horizontal spheroid, and vertical spheroid are selected. Effects of impact angle, initial droplet shape, and film thickness on the impact outcomes are mainly studied. Results show that the liquid crown seems to be a beveled round tube in the case of sphere droplet impact. In contrast, it seems to be a ship in the case of vertical spheroid droplet impact, and the liquid crown is less asymmetry for the horizontal spheroid droplet impact. When the Weber number exceeds the critical value, secondary droplets will detach from the rim of the liquid jets. The number and size of the secondary droplets are associated with the impact droplet shapes. For the sphere droplet impact case, the crown radius and the crown height on the front side of the advancing droplet (right side) increase with the impact angle. With an increase in the film thickness, the right crown radius decreases, while the right crown height first increases and then decreases. [ABSTRACT FROM AUTHOR]

The low-velocity impact behavior of carbon-epoxy cross-ply composites was numerically investigated, examining the effect of impact angle. A plastic continuum damage model, introducing the cohesive interface to describe delamination damage, was established and was validated by available experimental data. Impact histories, progressive deformation, stress transfer, and impact damage are respectively discussed. The results show that an increase in impact angle intensifies the action of tangential force, and gradually transfers energy absorption from normal plastic deformation to tangential deformation and friction, which dissipates more energy through relatively longer contact duration and larger impactor displacement. The delamination damage to upper layers is more affected by tangential loads, intensifying with the increase of the impact angle, and the damage area to the top interface is increased by 132.1% from 0° impact to 60° impact. Meanwhile, the delamination damage to lower layers is mainly determined by normal loads, weakening with the increasing impact angle overall, and the damage area of the lowest interface decreases by 36.6% from 0° impact to 60° impact. [ABSTRACT FROM AUTHOR]

Damage induced by coarse particle erosion is the main cause of premature failure of transport structures used in deep-sea mining. In this study, a free fall coarse particle stress-erosion (i.e., the erosion of a highly stresses target material) test method is proposed as an alternative to the traditional impinge jet test. The erosion behavior of stainless steel SS304 under different loads and impact angles was experimentally studied. The related mass loss was quantified, the microscopic wear morphology was observed and the erosion mechanism was revealed. This study indicates that the erosion damage caused by coarse gravels is much severer than that caused by fine sands, while the stress-acceleration effect (generally, the erosion damage will be enhanced when the target material is suffering from high tensile stress) of SS304 is relatively marginal. Finally, the validity of some widely used erosion equation was examined by the test data. [ABSTRACT FROM AUTHOR]

Herein, the influence of the impact angle and Ni content on the wear behavior of Mo 2 NiB 2 –Ni cermets was studied using an erodent-carrying slurry comprising artificial seawater and SiO 2 sands. The results reveal that the material loss may be attributed to the wear damage caused by SiO 2 sands because cermets are expected to exhibit good corrosion resistance in artificial seawater. The relative density of cermets markedly influences their resistance to wear damage, and the material loss experienced by cermets with poor relative density is 2–4 times higher than that of cermets with good relative density; this occurs because a higher relative density can markedly enhance the mechanical properties and reduce the defects in the cermets. Moreover, the results indicate that as the impact angle increases from 0° to 60°, the manifestation of the wear mechanism changes from damaging the Ni binder phase (caused by single cutting wear) to damaging both the Mo 2 NiB 2 ceramic and Ni binder phases due to the combination of cutting wear and impact wear. The wear damage is dominated by the cutting wear and impact wear from SiO 2 sand at the low and high impact angles, respectively. Furthermore, the severe deterioration of the single ceramic skeleton at high impact angles indicates that the synergistic influence of the Mo 2 NiB 2 ceramic and Ni binder phases on enhancing the wear resistance of the cermets intensifies at high impact angles. [ABSTRACT FROM AUTHOR]

The mechanical response of CFRP laminates under low-velocity oblique impact was investigated using finite element simulation and experimental test in this paper. Based on the 3D Hashin failure criterion, bilinear cohesive constitutive model and progressive failure theory, a finite element model of CFRP laminate with hemispherical cylindrical impactor under low-velocity oblique impact was established, by using finite element simulation software ABAQUS. A clamp for multi-angle impact was designed and manufactured. A low-velocity oblique test platform was built based on the clamp. Several groups of experiments with different impact angles and impact energy were carried out. It was found that the damage morphology and energy absorption caused by normal impact and oblique impact is quite different. For normal impact, the main damage mode on the front of the laminate is indentation, while for oblique impact, the main damage mode on the front surface is scratch due to the sliding of the impactor on the laminate. The damage caused by normal impact on the back of the laminate is always more significant than that caused by oblique impact. The simulation results of the contact force and the residual velocity of impactor are compared with the experimental results, and the good agreement verifies the reliability of the simulation model. The mechanical response is studied by simulation, and it is found that the mechanism of normal impact is different from that of oblique impact. The contact force and residual kinetic energy of the impactor decrease with the increase of impact angle, while the contact time and the energy consumed by friction increase are the opposite. The energy absorbed by the laminate is not negatively related to the impact angle. [ABSTRACT FROM AUTHOR]

Impact direction is one of the critical factors affecting the waterdrop erosion behavior of materials. In this paper, rain erosion damage behavior of a typical carbon fiber reinforced polymer (CFRP) laminate is investigated as a function of the impingement angle (0° as normal impact and 15°, 30°, 45° as oblique impact deviated from the normal) and the relative fiber orientation (parallel PA and perpendicular PE to the fiber direction of the surface layer) under the waterjet velocity of 320 m/s and the impact frequency of 50 Hz via a pulsating waterjet erosion test rig. After continuous impact of multiple waterjets, the typical damage of CFRP laminates is mainly composed of the central erosion crater and the upheaval of the surrounding surface layer. The onset and evolution of damage are mainly driven by the shear action of lateral jetting and stress concentration of hydraulic penetration exerted at the surface irregularities. There is no significant difference in the damage modes between the normal and oblique impacts, except for the asymmetric distributions of matrix cracking in PA-orientation and delamination in PE-orientation caused by the angle inclination. With the impingement angle increasing, the volume loss and erosion depth decrease while the incubation period increases mainly due to the decreases of water hammer pressure and contact area. The PA-orientation can cause lower incubation period and larger erosion mass loss than PE-orientation before the surface ply is penetrated, with the underlying mechanism related to the distinct tensile properties of CFRP laminates along longitudinal and transversal directions and the asymmetric properties of fiber–matrix interface. According to the fitting results of erosion curves, it is possible to describe the incubation period and the erosion rate of CFRP laminates under oblique impact using a two-branch equation, and Springer model can give reasonable prediction for the average incubation period and PA-orientation erosion rate of a certain oblique impact occasion with known 0° impact erosion results. [ABSTRACT FROM AUTHOR]

Conventional guidance law designs can only guarantee steady-state performance. However, transient performance is also the key performance index in practical guidance applications. In this paper, a novel terminal guidance law is presented for missile intercepting maneuvering target with impact angle constraints, which can strictly guarantee the prescribed steady-state and transient performances of interception. By utilizing the prescribed performance control technique, the prescribed performance tracking control problem is transformed into an equivalent unconstrained form such that the tracking error can be limit to the prescribed performance bound. Then, on the basis of transferred the tracking error, a novel nonsingular terminal sliding mode control-based guidance law is proposed with impact angle constraint, and the extended state observer is incorporated to online estimate the external disturbances and unknown target maneuver. The closed-loop system stability and the convergence characteristic are rigorously proved. Finally, extensive contrast simulations are conducted to demonstrate the efficiency and superiority of the proposed guidance law for different engagement scenarios. [ABSTRACT FROM AUTHOR]

To intercept maneuvering target considering impact angle constraint and actuator faults, a novel three-dimensional (3D) guidance law is proposed in this paper. To guarantee the interception, the multi-variable super-twisting-algorithm-like (STA-like) is adopted in the proposed guidance law, so as to drive the line-of-sight (LOS) angle to the desired value and its rate to zero in finite time in both pitch and azimuth directions. However, it is usually a difficult task for STA-like to select the proper design parameters, and the necessary disturbance gradient for STA-like is also not clearly known, owing to realistic actuator faults and the independence between missile and target. Moreover, the actuator faults in this paper are formulated as disturbances in the control scheme, and the necessary disturbance gradient for STA-like is not clearly known as well. To solve these problems, a multi-variable dual-layer adaptive scheme is employed to adjust the control gains and guarantees its precision. The theoretical analysis and numerical simulation results demonstrate the effectiveness of the proposed guidance law. The combination of STA-like and adaptive theory in the presented guidance law for the first time can guarantee the successful interception and can generate precise and robust control signal simultaneously with impact angle constraint and actuator faults consideration.

Based on adaptive sliding mode control method, this paper considers the interception problem to deal with both impact time and angle constraints. The stability and convergence characteristic of proposed guidance law are analyzed. The requirements of the terminal constraints and minimum miss distance can be satisfied. An adaptive law is put forward to adjust the guidance gain. The simulation results indicate that the missile with proposed guidance law can intercept the target successfully with not only desired impact time but also expected impact angle. The interception task can be fulfilled in a satisfactory manner.

In this paper, a red-eared slider turtle is used as the prototype for the bionic design of the foamed silicone rubber sandwich structure. The effect of impact angle on the performance of the foamed silicone rubber sandwich structure against low-velocity impact is studied by the finite element method. The numerical model uses the intrinsic structure model of foamed silicone rubber with porosity and the three-dimensional Hashin fiberboard damage model. The validity of the model was verified after experimental comparison. Based on the finite element simulation of different impact angles and velocities, the relationship between impact velocity and residual velocity, as well as the penetration threshold at various impact angles are obtained, and the change law of impact resistance of foamed silicone rubber sandwich structure with impact angle and velocity, as well as the damage pattern of sandwich structure at different impact angles and velocities are given. The results can provide a basis for the impact resistance design of the bionic foamed silicone rubber sandwich structure. The results show that, at a certain impact speed, the smaller the impact angle, the longer the path of the falling hammer along the plane of the sandwich structure, the lighter the damage to the sandwich structure and the greater the absorbed energy, so that avoiding the impact from the frontal side of the sandwich structure can effectively reduce the damage of the sandwich structure. When the impact angle is greater than 75°, the difference in impact resistance performance is only 2.9% compared with 90°, and the impact angle has less influence on the impact resistance performance at this time.

The first point of contact between a spherical blood drop and a surface is related to the angle between the trajectory of the blood drop and the surface being struck. This angle is often referred to as the impact angle which can be estimated by knowing the width and length of the resultant elliptical bloodstain. Most software programs dedicated to area of origin analysis indicate the location of the backtracked bloodstain trajectory to be at the geometric centre or at the tip of the bloodstain ellipse. However, it is unknown how the first point of contact and the blood drop trajectory (here defined as the locus of the centre of mass of the drop as it travels) are related empirically. Thus, this study aims to look at how the initial point of contact and the trajectory at the impact of a blood drop relates to the formed bloodstain ellipse. Two volumes of blood (0.013 ml and 0.071 ml) were dropped from a height of 10 cm and 40 cm onto an inclined surface at 0°, 15°, 30°, 45°, 60°, and 75°. The transition from a spherical blood drop to an elliptically shaped bloodstain was recorded using a high-speed camera for all tests. A total of 72 ellipses were analyzed to determine the location of the first point of contact and trajectory point of the blood drop and how they relate to the formed elliptical bloodstain. A relationship was found between the first point of contact and the bloodstain trajectory which was dependent on the impact angle. However, there were clear deviations from theoretical assumptions due to blood drop oscillations, the effects of gravity, and the natural fluid characteristics of blood. The results of this study may assist bloodstain pattern analysts and software developers by more accurately applying the location of the blood drop trajectory based on empirical data. • The first point of contact follows a similar trend to the sine value. • The trajectory point moves along the half-length of the bloodstain. • The trajectory point and first point of contact are mainly at different locations. • The trajectory point is not always at the centre or tip of the ellipse. • The first point of contact is not always at the centre of tip of the ellipse. [ABSTRACT FROM AUTHOR]

To improve the penetration capability and the damage effectiveness of cruise missiles, maneuvering trajectory with specific impact angle is applied in terminal guidance. In this paper, an innovative online method for terminal guidance is presented, which can guide the cruise missile to a stationary target along a climb-and-dive maneuvering trajectory while meeting the expected impact angle. The basic principles of the proposed guidance method are the Bézier curve theory and the missile inverse dynamics. The maneuvering trajectory is shaped by a third-order Bézier curve based on the missile current state, the target position, and the impact angle constraint. The real-time guidance command represented by attack angle $\alpha $ is obtained based on the missile inverse dynamics. The shape of flight trajectory can be modified by regulating the Bézier parameters $b_{1}$ and $b_{2}$ to satisfy different tactical requirements without changing the boundary conditions. Simulation results demonstrate the effectiveness of the proposed method applied in cruise missile terminal guidance.

In this paper, a three-dimensional (3D) impact-angle-control guidance law is proposed based on the approaches of nonsingular terminal sliding mode control and fixed-time convergence theory to intercept a maneuvering target. The guidance law is derived based on the coupled 3D engagement dynamics. To intercept the target with an expected impact angle, the nonsingular terminal sliding mode control is designed to ensure that the line-of-sight (LOS) angles and rates rapidly reach the desired values. Furthermore, the fixed-time convergence algorithm is proposed to guarantee that the LOS angles and rates are convergent in fixed time. The upper bound of the settling time can be obtained by presetting the parameters of the proposed guidance law, and it is independent of the initial conditions. The stability of the guidance system is proven via Lyapunov stability theory. The simulation results are presented to validate the efficiency and superiority of the proposed guidance law.

Considering the velocity of the missile cannot remain constant in most applications due to the effect of aerodynamic drag and thrust, a feasible adaptive impact angle control guidance law under varying velocity is proposed. The design of the guidance command is transformed into the design of the flight path angle, which is proposed as a general polynomial function of time-to-go with unknown coefficient. In addition, the unknown coefficient can be acquired from the boundary condition of the position. To cope with unpredictable disturbances, the adaptive scheme to initialize and recalculate the control parameter at each time step is also adopted. First, the guidance law is proposed with constant velocity. Then the law is extended to a more practical situation by considering varying velocity, and the estimation of time-to-go under varying velocity is proposed. Different simulations are carried out to verify the performance of the proposed guidance law.

The low-velocity impact behavior of carbon-epoxy cross-ply composites was numerically investigated, examining the effect of impact angle. A plastic continuum damage model, introducing the cohesive interface to describe delamination damage, was established and was validated by available experimental data. Impact histories, progressive deformation, stress transfer, and impact damage are respectively discussed. The results show that an increase in impact angle intensifies the action of tangential force, and gradually transfers energy absorption from normal plastic deformation to tangential deformation and friction, which dissipates more energy through relatively longer contact duration and larger impactor displacement. The delamination damage to upper layers is more affected by tangential loads, intensifying with the increase of the impact angle, and the damage area to the top interface is increased by 132.1% from 0° impact to 60° impact. Meanwhile, the delamination damage to lower layers is mainly determined by normal loads, weakening with the increasing impact angle overall, and the damage area of the lowest interface decreases by 36.6% from 0° impact to 60° impact.

In this article, two cooperative guidance schemes with impact angle and time constraints are proposed for multiple missiles cooperatively intercepting a maneuvering target in the presence or absence of a leader missile. First, cooperative interception with impact angle constraint is formulated based on the relative motion equation between the interceptors. Subsequently, the design of the guidance law is divided into two stages. In the first stage, based on finite-time consensus theory and the super-twisting control algorithm, the cooperative guidance law in the direction of the line of sight (LOS) is derived to control the impact time so that all missiles can simultaneously intercept the target in finite time. Then, based on finite-time sliding mode control and the super-twisting control algorithm, a finite-time convergence cooperative guidance law in the normal direction to the LOS is developed to control the intercept angle and the LOS angle rate so that each missile can accurately hit the target at a desired angle. Finally, by controlling the consensus error of flight time in the presence of a leader missile, a finite-time cooperative guidance method in the “leader–follower” scenario is derived for simultaneous arrival at the target. The proposed methods can effectively suppress chattering and ensure fast convergence in finite time. Simulation experiments are conducted to verify the effectiveness of the proposed cooperative guidance schemes. [ABSTRACT FROM AUTHOR]

The mission of simultaneous attack and warhead lethality enhancement requires the constraints on impact time and angle in the guidance design. To this end, a two-stage guidance law considering constrained impact as well as the robustness against external disturbances and heading errors is proposed. The first stage is based on a circle involute geometrical rule that guarantees the desired velocity direction at the involute's end. With this goal achieved, the involute guidance is switched to the guidance of nullifying line-of-sight rate such that near-zero maneuver in the second stage is ensured. To achieve both impact time and angle constraints, a simple parameter determination approach is provided to find explicit solutions for the desired two-stage trajectory. Meanwhile, a robust two-stage guidance law is constructed to implement the geometrical rule, guarantee terminal constraints, and ensure robustness. The proposed technique is easy to implement, in that it does not involve model linearization, time-to-go estimation, and numerical optimization routine. Additionally, the achievable range of different constraints is analyzed considering practical issues such as initial launch angles, initial line-of-sight angles, and acceleration limits. Extensive simulations are carried out in various engagement scenarios under uncertainties and disturbances to validate the effectiveness and robustness of the proposed guidance law. [ABSTRACT FROM AUTHOR]

Magnetic pulse welding is a solid-state joining technology, based on the use of electromagnetic forces to deform and to weld workpieces. Since no external heat sources are used during the magnetic pulse welding process, it offers important advantages for the joining of dissimilar material combinations. Although magnetic pulse welding has emerged as a novel technique to join metallic tubes, the dimensional consistency of the joint assembly due to the strong impact of the flyer tube onto the target tube and the resulting plastic deformation is a major concern. Often, an internal support inside the target tube is considered as a solution to improve the stiffness of the joint assembly. A detailed investigation of magnetic pulse welding of Cu-DHP flyer tubes and 11SMnPb30 steel target tubes is performed, with and without an internal support inside the target tubes, and using a range of experimental conditions. The influence of the key process conditions on the evolution of the joint between the tubes with progress in time has been determined using experimental investigations and numerical modelling. As the process is extremely fast, real-time monitoring of the process conditions and evolution of important responses such as impact velocity and angle, and collision velocity, which determine the formation of a metallic bond, is impossible. Therefore, an integrated approach using a computational model using a finite-element method is developed to predict the progress of the impact of the flyer onto the target, the resulting flyer impact velocity and angle, the collision velocity between the flyer and the target, and the evolution of the welded joint, which are usually impossible to measure using experimental observations. [ABSTRACT FROM AUTHOR]

Nonsingular terminal sliding mode (NTSM) guidance for intercepting the desired line of sight (LOS) angle in terminal phase is proposed in this paper. In order to satisfy the predefined LOS angle and to intercep into target, a nonsingular terminal sliding variable is introduced. In reaching phase, in the presence of uncertainties such as target maneuvers, robust NTSM guidance law is designed in order forzeroing the sliding variable in finite reaching time. Then, in sliding phase, due to introducing nonsingular terminal sliding variable, finite time stability of line of sight angle and line of sight angular rate is granteed without singularity in commanded acceleration as control signal Numerical simulations are presented to illustrate the potential of the proposed guidance law.

This paper addresses a novel impact time and angle control guidance law using a Bézier curve. The 2nd order Bézier curve consists of one control point and two boundary points; initial point P0, middle point P1 and end point P2. The curve is tangent to the line P0-P1 and the line P1-P2, respectively, and always exists in the convex hull of the control points. Proposed Bézier curve navigation guidance, makes the missile follow the Bézier curve with the feedback form of guidance command so that the missile hits the target on the desired time in the desired direction. We conducted numerical simulations on several terminal conditions to demonstrate the performance of proposed method.

The wear of induction cladded coating during motion was investigated through the abrasive mass at a speed of 1.0 to 3.0 m/s and the impact angle of abrasive particles with a worn surface of 0° to 90°. Cladding was performed by using Ni-Cr-Si-B-Fe flame spraying powder. Experimental research was carried out by using the Response Surface Method (RSM) and Central Composite Design (CCD). Analysis of variance proved that both motion speed and impact angle had significant impact on the wear of coating, both individually and interactively. Motion speed had the greatest influence, and the interaction of speed and angle had the least influence. The wear rate increased along with the motion speed increase, and the influence of the impact angle depends on the wear speed. At a speed of 1 m/s, the wear increases along with the increase of angle from 0° to 45° and then continues to decrease up to the angle of 90°. At a speed of 2 m/s, the wear increases along with the angle increase from 0° to 30° and then continues to decrease up to the angle of 90°. At a speed of 3 m/s, the wear increases along with the angle increase from 0° to 20° and then decreases as the angle increases up to 90°. Based on the statistical data processing, this research developed the mathematical model of wear in the form of quadratic polynomial that describes the influences of input variables in individual and interactive form.

For the elasto-plastic contact-impact problems of a vertical rod-like structure imparting the fixed oblique flat surface, the dynamics equations of the rod-like structure and the formulations of instantaneous contact forces in each phase during contact-impact events were established, and the vat nous laws of the motion parameters and the contact forces were systematically studied in detail. Using ODE45 function, the time-variation laws such as the kinetic energy of the rodlike structure, position and velocity of the contact point, angle and angular velocity of the rodlike structure were analyzed. Besides, the relationships between the coefficient of restitution and the initial impact velocity, and the permanent deformations depending on initial impact velocity, as well as the contact forces with the contact deflection, were also achieved by the numerical analyses. The results show that the higher the initial drop height, the shorter the contact-impact time and the more obvious the rebounding phenomenon. And the contact force vs. contact deflection curves show similar trends with increasing initial drop height, but the permanent deformations are closer to the maximum deformation. Contact-impact tests were performed by dropping the vertical rounded ended rodlike structure from different initial drop heights on the fixed oblique flat suffice with the inclination angle of 45°, and then, combined with testing data for the coefficient of restitution and permanent deformation in normal impact events reported in literatures, the comparative analysis results show that the simulation results are basically match with the testing results, which is verified the accuracy of the established model. [ABSTRACT FROM AUTHOR]

Erosion-corrosion behaviour of pure Tantalum (Ta) was investigated using corrosive slurry solutions (pH 4, 7, and 10) containing 7 wt% SiC as erodent particles. Tests were carried out using an impinging jet erosion-corrosion apparatus with a jet velocity of 5 ms−1 and at two impact angles (30° and 90°). Under particle bombardment conditions, a marked reduction in corrosion resistance offered by Ta was observed amid a significant cathodic shift in the E Corr values for all pH values investigated. Results showed that interaction between erosion and corrosion was higher under 30° impact leading to a higher rate of material removal. On the contrary, negative synergism was observed for experimental conditions of normal impact for pH 7 and pH 10. Scanning electron microscopy studies revealed typical ductile erosion mechanisms of material removal which consisted of dominating micro-cutting for 30° and plastic deformation resulting in lip formation for normal impact angle. These appeared to be assisted by dissolution of weakened areas and passive layer removal as corrosion mechanisms. Potentiostatic erosion-corrosion experiments were utilised for calculation of synergistic and antagonistic effects and have been presented in the paper. • Significant reduction in aqueous corrosion resistance under particle bombardment. • Erosion-corrosion interaction higher at 30° impact than at 90° irrespective of pH. • Additive effect (erosion assisting corrosion) found for 90° impact for pH 4. • Antagonistic effect (reduction in erosion due to corrosion) for pH 7 & 10 at 90° impact. • Wear mechanisms resemble ductile-erosion behaviour further assisted by corrosion. [ABSTRACT FROM AUTHOR]

This paper presents an investigation of abrasive waterjet turning (AWJT). The purpose of the article was to investigate significant parameters of the turning process and to evaluate their impact on the turning product. The influence of the traverse speed, the rotational speed, and the relative position of the jet to the specimen (lateral jet shift) were investigated. Based on the previous research done in this field, the multi-pass tangential turning method was selected. Rotational speed does not seem to have a significant impact on the AWJ turning process. However, the relative position of the jet is a key parameter for improving the efficiency of the process. Increasing the lateral jet shift causes the volume of the material removed to increase until the optimal impact angle is reached. These findings need to be extended in order to adjust AWJT. Without these improvements, a comparison of jet to traditional technologies is inappropriate.

In this paper, we present an observer-based partial integrated guidance and control (PIGC) scheme for missiles to achieve hit-to-kill attack at a given impact angle. This is particularly useful as the lethality of a missile can be maximized if collision occurs at a certain angle. A novel sliding mode observer is proposed to estimate all states of the system in finite time, from which the PIGC is designed to make all states converge to zero and achieve the objective. The observer parameters are automatically updated by adaptive laws, which removes the requirement of knowing the bound of disturbances and hence making the scheme more applicable to real missile systems. [ABSTRACT FROM AUTHOR]

The present contribution aims to examine the erosion behavior of soda-lime-silica glass in connection with damage interaction and angle effects. Experimental observations are reported on glass plates subjected to sandblasting process using alumina abrasive particles for different sandblasting durations and impact angles. The damage and erosion mechanisms are computed through a numerical model of the sandblasted glass plate. The glass internal stiffness degradation due to impact process is accounted for by an anisotropic stress-based continuum damage mechanics model. The glass erosion is simulated by means of a vanishing element technique using the critical values of damage components as failure criterion. A parametric numerical study is carried out to bring insights into damage interaction and angle effects on the material loss. [ABSTRACT FROM AUTHOR]

Abstract Glass fiber aluminium laminate (GLARE) is a kind of fiber metal laminates widely applied in aircraft structures, frequently subjected to low-velocity impact incidents. The purpose of this paper is to investigate the dynamic response and damage mechanism characterization of GLARE under single and repeated low-velocity impacts. Firstly, a progressive degradation finite element (FE) model was developed and validated. Three different failure criteria were compared to analyze the damage behavior of composites of GLARE in terms of accuracy and efficiency, wherein a user defined material subroutine VUMAT was introduced. Then, the validated model was used to study the influence of the impact angle. Four different impact angles including 30°, 45°, 60° and 90° were analyzed in terms of plastic deformation, impact contact force, energy absorption and internal damage. Finally, the simulation of GLARE subjected to repeated impacts was carried out, in which the cumulative damage effects were considered. The detailed dynamic response and damage evolution of aluminium layers and composite layers as well as their interfaces with the number of impacts increasing were revealed. [ABSTRACT FROM AUTHOR]

Abstract A new guidance law with both impact time and impact angle constraints is proposed in this paper. We first simplify missile dynamics under small heading error approximation, and derive an optimal guidance law with impact angle constraint against a stationary target. By adding a feedback controller to the obtained optimal guidance law, both impact time and angle requirements are achieved and the singularity problem is tackled. The proposed guidance law can be used to perform a simultaneous formation cooperative attack. Numerical simulations are demonstrated to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]