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This theoretical work deals with delamination in U-shaped load-carrying structural members. The latter represent multilayered functionally graded systems of non-linear viscoelastic behaviour. The right-hand vertical part of the structure under consideration is delaminated. The structure is clamped in the lower end of the left-hand vertical part. Besides, the structure is supported by a rotational spring which has non-linear elastic behaviour. The strain energy release rate is derived by using an approach that is based on analysis of equilibrium of the various components of the U-shaped structure. The solution derived is checked-up by applying the method of the integral J. The dependence of the strain energy release rate on different parameters is studied and presented in form of various graphs. Analysis of a U-shaped structural member with two rotational spring supports also is carried-out and the strain energy release rate obtained is compared with that in the U-shaped structure with one rotational spring support. [ABSTRACT FROM AUTHOR]

This theoretical work deals with delamination in U-shaped load-carrying structural members. The latter represent multilayered functionally graded systems of non-linear viscoelastic behaviour. The right-hand vertical part of the structure under consideration is delaminated. The structure is clamped in the lower end of the left-hand vertical part. Besides, the structure is supported by a rotational spring which has non-linear elastic behaviour. The strain energy release rate is derived by using an approach that is based on analysis of equilibrium of the various components of the U-shaped structure. The solution derived is checked-up by applying the method of the integral J. The dependence of the strain energy release rate on different parameters is studied and presented in form of various graphs. Analysis of a U-shaped structural member with two rotational spring supports also is carried-out and the strain energy release rate obtained is compared with that in the U-shaped structure with one rotational spring support.

Approximating functions are used in calculating the stress–strain state of a three-layer cylindrical shell by means of Maple software. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity and compactness conditions on the components of the model, it is proved that the value of the game satisfies an equilibrium equation, and the existence of a Nash equilibrium is established. [ABSTRACT FROM AUTHOR]

Grouting is widely used to solve problems such as water inrush and collapse in tunnels and subways, with permeation grouting being the most common method. This study explores the influence of fluid flow resistance on the permeability of porous media and derives an analytic expression for the variation of permeability in porous media based on the diffusion law of cement-based grout columns-hemispherical diffusion. Based on this, a Newtonian fluid permeation grouting column-hemispherical diffusion model considering the variation of permeability in porous media is established, combining the rheological equation and the equilibrium equation of the Newtonian fluid. The theoretical results considering the influence of fluid flow resistance on the permeability of porous media are consistent with the results of existing laboratory tests and numerical simulations, which are closer to the experimental results, thus verifying the effectiveness of the proposed theoretical mechanism. Parameter analysis shows that with the increase of grouting pressure and grouting time, the diffusion radius of the Newtonian fluid infiltration grouting, considering the variation of permeability in porous media, increases rapidly and then increases slowly, and with the increase of porous media porosity, its radius decreases gradually. The research results can provide theoretical support for selecting grouting parameters and quality control in porous media infiltration grouting engineering practice.

Research on the mechanical properties of transverse constraint force of anchor support under different loads can help to improve work safety. In this paper, based on the higher-order shear deformation theory, the higher-order whole-local theory of anchor rods is established with full consideration of the transverse normal strain. The geometric and physical equations in the intrinsic relationship are given for the wet thermodynamic behavior of anchor rods’ transverse restraining force. The equilibrium equations of the whole-local are constructed by combining them with the principle of virtual displacement. The analytical solution of the anchor core material was calculated by applying Navier’s method. The boundary displacement conditions of the anchor core material were solved. The anchor core material was modeled by combining it with ABAQUS finite element software. The mechanical analysis was carried out from the two perspectives of the buckling problem under thermal load and the parameter change of the transverse restraining force, respectively. It was found that when the thickness of the anchor bar increased from 20 mm to 50 mm, the radial displacement of the upper layer decreased by 52.95%, and there was no significant change in the positive stress at the upper and lower interfaces. The peak value of the upper interface shear stress decreases significantly from 0.55MPa to −1.41MPa when the anchor laying method is changed from a single layer to four layers. The combination of higher-order theory with ABAQUS software can effectively analyze the change of transverse constraint force of the anchor support, which can help improve its safety.

This paper approximately analyzes the dynamic response mode of building materials under impact load according to the Lagrange equation. We use the redundant constraint force of the statically indeterminate structure to list its strain energy expression. At the same time, the paper introduces the Lagrange multiplier and combines the static equilibrium equation to obtain the internal force of the statically indeterminate structure. The calculation results show that the load duration and peak value are important factors determining structural members’ failure mode. This study lays the foundation for the research on the structural building material’s dynamic control and mechanism performance. At the same time, our research results also provide methods and ideas for the rigid body dynamics modeling of other structural redundant parallel mechanisms.

Purpose: In this paper, the main factors influencing the structure stiffness will be analyzed by studying the tangent stiffness matrix based on different requirement in engineering practice. The authors can obtain the deformation of three-bar tensegrity basic unit in different load, and gain the primary factor by comparing the deformation, which will provide reference to concrete structure design in the engineering. Design/methodology/approach: The mathematical model of tensegrity structure was built by establishing generalized node coordinates and connective matrix. Three main factors that affect the structure deformation can be obtained by analyzing the stiffness matrix, which is preload, Young's modulus, and cross-sectional area, the thinking of deformation also be sorted out. The deformation analysis of the concrete structure is carried out, and it is concluded that increasing the cross-sectional area can quickly improve the stiffness of the structure, which provides a reference for the structural variable stiffness design in practical engineering. Findings: (1) When the axial external force is applied to the structure, the torsion-angle deformation of the structure is the largest, and the radial deformation of the structure is the smallest. (2) The structure stiffness can be rapidly enhanced by increasing the cross-sectional area. But the cross-sectional area can't be increased indefinitely. Because the mass will be increased once increasing the cross-sectional area, which will destroy the structure of the advantages of light weight in engineering practice. Originality/value: The deformation analysis of the concrete structure is carried out, and it is concluded that increasing the cross-sectional area can quickly improve the stiffness of the structure, which provides a reference for the structural variable stiffness design in practical engineering. [ABSTRACT FROM AUTHOR]

On the basis of the force and safety factor analysis of traditional retaining walls, a new analytical method of force and displacement of the slope is suggested, the numerical theoretical solution of the stress distribution of the sliding body can be obtained under the conditions, which the stresses distribution are satisfied with the differential equilibrium equations, the boundary conditions, the compatibility equation and the macroscopic equilibrium equations. The interface stresses between the sliding body and the retaining wall is continuous, and the theoretical solution of retaining wall stress distributions can be obtained, while the stress differential equilibrium equation, the compatibility equation, macroscopic force, and moment balance equations are satisfied. The strain and displacement solutions can be obtained by using Duncan Chang and Hooke constitutive equations for the slope and the retaining wall, respectively. The transfer station of landfill in the Guandukou Town of Badong County is taken as an example, the results of the sliding body and retaining wall analysis show: The stress and strain solutions of a slope and a retaining wall can be obtained by the proposed method. The anti-slip force of the retaining wall calculated by the method in this paper contains the positive pressure and shear force along the contact surface and varies with the deformation of the slope, in addition, the numerical theoretical solution of the retaining wall shows that the retaining wall shape and material can be optimized according to the calculation results. It is feasible for the proposed analysis method of slope with retaining wall design to be run many years. [ABSTRACT FROM AUTHOR]

The effectiveness of piles with reverse surface slope in frost heaving of soil has been the subject of discussion in many papers. In the previous works, the author considered cylindrical piles with an upper reverse taper and calculation method for the piles under these conditions. However, in order to extend the area of their use it is necessary to consider other configurations of piles as well. In this study, prismatic face slope piles are modeled for soil frost heaving conditions; equilibrium equations for calculating prismatic piles with four, six and eight faces are derived. The equilibrium equation for prismatic face slope piles in general form is also given. The equations make it possible to determine geometric parameters of piles ensuring their stability in soil under the action of tangential frost heaving forces. The author analyzes material capacity of cylindrical taper piles and prismatic face slope piles. The piles have the same bearing capacity in thawed soil and operate under the same geological and climatic conditions set before. The square pile with a sloping face shows the lowest material capacity. The proposed approach can be used for prismatic piles with a different number of faces in various conditions.

In large-scale wind turbines, the force state of the pitch system greatly influences safe operation and service life. This paper provides a novel method to estimate blade pitch load, bearing friction torque, and motor pitch torque. In this method, the force equilibrium equations are established by investigating the force of the pitch system under multiple operating conditions. The multidimensional BIN method is employed to classify the supervisory control and data acquisition (SCADA) data of wind turbines into several intervals. The multidimensional scatter data is processed in a single-valued way. Then, the estimating model of the pitch system forces is established by combining the obtained data and the equilibrium equations. Taking a 2 MW wind turbine as an example, the variation characteristics of blade pitch load, bearing friction torque, and motor pitch torque under multiple operating conditions are analyzed. Some interesting and valuable conclusions are obtained. For example, when the wind speed increases, the blade pitch load increases significantly in the maximum wind energy tracking region, but there is no obvious change in the observed constant power output region. The wind speed and azimuth have little effect on the bearing friction torque. The variation trend of motor pitch torque is consistent with that of blade pitch load in the maximum wind energy tracking region.

Analytical formulations and solutions for the thick rectangular plate static analysis with clamped support based on a three-dimensional (3-D) elasticity theory is developed using the energy method. The theoretical model, whose formulation is based on the static elastic principle as already reported in the literature, is presented herein to obviate the shear correction coefficients while considering shear deformation effect and transverse normal strain/stress in the analysis. The equilibrium equations are obtained using 3-D kinematic and constitutive relations. The deflection and rotation functions, which are the solutions of the equilibrium equation, are obtained in closed form using a general variational technique for solving the boundary value problem. The minimization energy equation yields the general equation which was used to obtain the theoretical model for the deflection and stresses of the plate. The results are compared with the available literature and the results-computed trigonometric displacement function shows that this 3-D predicts the vertical displacement and the stresses more accurately than previous studies considered in this paper. The result showed that the percentage difference between the present work and those of 2-D Mindlin FSDT, 2-D numeric analysis, and 2-D HSDT of polynomial shape functions was about 3.02%, 0.62%, and 0.33%, respectively. It is concluded that the 3-D trigonometric model gives an exact solution, unlike other 2-D theories, and can be used for clamped-supported thick plate analysis. Doi: 10.28991/HIJ-2022-03-03-03 Full Text: PDF

On the basis of the force and safety factor analysis of traditional retaining walls, a new analytical method of force and displacement of the slope is suggested, the numerical theoretical solution of the stress distribution of the sliding body can be obtained under the conditions, which the stresses distribution are satisfied with the differential equilibrium equations, the boundary conditions, the compatibility equation and the macroscopic equilibrium equations. The interface stresses between the sliding body and the retaining wall is continuous, and the theoretical solution of retaining wall stress distributions can be obtained, while the stress differential equilibrium equation, the compatibility equation, macroscopic force, and moment balance equations are satisfied. The strain and displacement solutions can be obtained by using Duncan Chang and Hooke constitutive equations for the slope and the retaining wall, respectively. The transfer station of landfill in the Guandukou Town of Badong County is taken as an example, the results of the sliding body and retaining wall analysis show: The stress and strain solutions of a slope and a retaining wall can be obtained by the proposed method. The anti-slip force of the retaining wall calculated by the method in this paper contains the positive pressure and shear force along the contact surface and varies with the deformation of the slope, in addition, the numerical theoretical solution of the retaining wall shows that the retaining wall shape and material can be optimized according to the calculation results. It is feasible for the proposed analysis method of slope with retaining wall design to be run many years.

The existence of solutions to the boundary value problem for a system of five nonlinear partial differential equations of the second order under given nonlinear boundary conditions is proved. This boundary value problem describes the equilibrium state of elastic shallow inhomogeneous anisotropic shells with unfixed edges in the framework of the Timoshenko shear model. The boundary value problem is reduced to a nonlinear operator equation in Sobolev space, the decidability of which is established using the contraction mapping principle. [ABSTRACT FROM AUTHOR]

This paper aims to apply the octonions to explore the torques and forces and so forth in the electromagnetic and gravitational fields, investigating the influences of material media on the equilibrium and continuity equations. The contemporary scholars utilize the quaternions and octonions to research the electromagnetic fields and gravitational fields and so forth. In this paper, the octonions are capable of surveying the electromagnetic and gravitational fields within material media, including the octonion field strength, field source, angular momentum, torque and force. Further, the octonion field strength and angular momentum can be combined together to become the octonion composite field strength, deducing the octonion composite torque and force and others. When the octonion composite force is equal to zero under certain circumstances, it is able to achieve eight equations independent of each other, including the force equilibrium equation, fluid continuity equation, current continuity equation and so on. The above reveals that the material media and octonion field strength can make a contribution to the eight equilibrium and continuity equations. And it is beneficial for deepening the understanding of equilibrium and continuity equations within material media. [ABSTRACT FROM AUTHOR]

The process of mechanized application of a binder polymer to the surface of fabric is considered. The thickness of the resulting polymer layer is determined when the fabric is pulled through a bath of polymer resin. The optimal speed of pulling the fabric is set. [ABSTRACT FROM AUTHOR]

This work is concerned with discrete-time Markov stopping games with two players. At each decision time player II can stop the game paying a terminal reward to player I, or can let the system to continue its evolution. In this latter case player I applies an action affecting the transitions and entitling him to receive a running reward from player II. It is supposed that player I has a no-null and constant risk-sensitivity coefficient, and that player II tries to minimize the utility of player I. The performance of a pair of decision strategies is measured by the risk-sensitive (expected) total reward of player I and, besides mild continuity-compactness conditions, the main structural assumption on the model is the existence of an absorbing state which is accessible from any starting point. In this context, it is shown that the value function of the game is characterized by an equilibrium equation, and the existence of a Nash equilibrium is established. [ABSTRACT FROM AUTHOR]

The impurity of Fe3+ in ammonium dihydrogen phosphate (MAP) solution has a significant influence on the morphology and quality of products. The removal of Fe3+ from the MAP solution by Di-(2-ethylhexyl) phosphoric acid (D2EHPA) was investigated in an impact-jet hydraulic cavitation (HC) extractor. The organic phase and aqueous phase can be highly mixed under the action of hydraulic cavitation. The extraction efficiency of 80% can be achieved when the extraction reaction was carried out for only 5 min. It was found that the extraction of Fe3+ with D2EHPA was an exothermic reaction, and the equilibrium equation of extraction was obtained by slope method as follows: Fe(aqu)3++8HD2(org)=FeD3·13HD(org)+3H(aqu)+After the two-stage extraction, the extraction efficiency of up to 96.7% can be reached (only 3.4 ∼ 4 ppm Fe3+ remained in the aqueous phase), and the MAP crystals with regular polyhedral structure, single phase nature, and high optical transmittance were obtained.

This work is concerned with discrete-time zero-sum games with Markov transitions on a denumerable space. At each decision time player II can stop the system paying a terminal reward to player I, or can let the system to continue its evolution. If the system is not halted, player I selects an action which affects the transitions and receives a running reward from player II. Assuming the existence of an absorbing state which is accessible from any other state, the performance of a pair of decision strategies is measured by the total expected reward criterion. In this context it is shown that the value function of the game is characterized by an equilibrium equation, and the existence of a Nash equilibrium is established. [ABSTRACT FROM AUTHOR]

This paper proposes a permeability function to estimate the water permeability coefficient of unsaturated soil. It is derived on the basis of the equilibrium equation of the water phase. Only one parameter is required in the proposed function, which is similar to the Brooks–Corey model. However, this parameter can be more easily obtained by using permeability tests of saturated soil with different porosity values. A number of test results in the literature are employed to validate the proposed permeability function, and the model prediction exhibits good agreement with the experimental data. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Effects of monovacancy formation on the charge states of nitrogen vacancy (NV) centers in nitrogen-doped diamond single crystal were investigated. Monovacancies are formed using high-energy electron beam irradiation. The ratio of the concentration of negatively charged nitrogen vacancy (NV−) centers to the total concentration of NV− centers and neutral nitrogen vacancy (NV0) centers decreases with increased concentration of monovacancies. This decrease occurs because of the reduction of the concentration of neutral substitutional nitrogen [N s 0] donating electrons to NV0 centers. Findings indicate that numerous electrons of N s 0 are transferred preferentially to monovacancies, not to NV0 centers. [Display omitted] • The preferential formation of N s + was observed with increased amount of monovacancy. • The formation of monovacancy in diamond leads to Fermi level downshift. • The NV− center population was found to decrease because of monovacancy formation. [ABSTRACT FROM AUTHOR]

Abstract In this short note, we correct some expressions obtained by Wang et al. (Bound. Value Probl. 2015:230, 2015). The corrected expressions will be useful for evaluating the boundary behaviors of solutions of modified equilibrium equations with finite mass subject. Moreover, the correction of Theorem 2.1 is also given.

In the development of previously obtained results for the case of average bending, a refined geometrically nonlinear theory of static and dynamic deformation of sandwich plates and shells with a transversely soft core and external composite layers with low rigidity for transverse shears and transverse compression was constructed. It is based on the use of the refined Tymoshenko's shear model for the carrier layers, taking into account lateral reduction, and for the transversally soft core, the simplified three-dimensional equations of the elasticity theory, which can be integrated along the transverse coordinate. The hypothesis of the similarity of the change laws of displacements across the thickness of the core during its static and dynamic deformation processes was adopted. When integrating the compiled equations of the elasticity theory to describe the stress-strain state, the two two-dimensional unknown functions are introduced that represent transverse shear stresses that are constant in thickness. Based on the generalized Lagrange and Ostrogradsky Hamilton variational principles for describing static and dynamic deformation processes with large indicators of the variability of the stress-strain state parameters, two-dimensional geometrically nonlinear equilibrium equations and general movements are constructed, which allow to reveal purely shear of buckling forms of the carrier layers during formation normal compressive stresses. [ABSTRACT FROM AUTHOR]

A mathematical model is proposed for the stress–strain state of a three-layer (sandwich) structure, taking account of nonlinear deformation of the supporting layers. Nonlinear deformation of a symmetric three-layer cylindrical shell under the action of transverse loads is considered, for different boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, the well-known Hencky problem—that is, the problem of axisymmetric deformation of a peripherally fixed and initially flat circular membrane subjected to transverse uniformly distributed loads—is re-solved by simultaneously considering the improvement of the out-of-plane and in-plane equilibrium equations. In which, the so-called small rotation angle assumption of the membrane is given up when establishing the out-of-plane equilibrium equation, and the in-plane equilibrium equation is, for the first time, improved by considering the effect of the deflection on the equilibrium between the radial and circumferential stress. Furthermore, the resulting nonlinear differential equation is successfully solved by using the power series method, and a new closed-form solution of the problem is finally presented. The conducted numerical example indicates that the closed-form solution presented here has a higher computational accuracy in comparison with the existing solutions of the well-known Hencky problem, especially when the deflection of the membrane is relatively large.