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Today digital qualification tools are part of many design processes that make them dependent on long and expensive simulations, leading to limited ability in exploring design alternatives. Conventional surrogate modelling techniques depend on the parametric models and come short in addressing radical design changes. Existing data-driven models lack the ability in dealing with the geometrical complexities. Thus, to address the resulting long development lead time problem in the product development processes and to enable parameter-independent surrogate modelling, this paper proposes a method to use images as input for design evaluation. Using a case study on the curtain airbag design process, a database consisting of 60,000 configurations has been created and labelled using a method based on dynamic relaxation instead of finite element methods. The database is made available online for research benchmark purposes. A convolutional neural network with multiple layers is employed to map the input images to the simulation output. It was concluded that the showcased data-driven method could reduce digital testing and qualification time significantly and contribute to real-time analysis in product development. Designers can utilise images of geometrical information to build real-time prediction models with acceptable accuracy in the early conceptual phases for design space exploration purposes. CC BY-NC-ND 4.0Copyright © 2023 Informa UK LimitedCONTACT Mohammad Arjomandi Rad radmo@chalmers.seReceived 20 Oct 2022, Accepted 29 Dec 2022, Published online: 19 Jan 2023The authors would like to acknowledge the staff in Autolivin Sweden for their participation in the project and also the Swedish Knowledge Foundation (KK-Stiftelsen with grant number 20180189) for the financial support.

Similar to parafoils, ram-air kites are flexible membrane wings inflated by the apparent wind and supported by a bridle line system. A major challenge in estimating the performance of these wings using a computer model is the strong coupling between the airflow around the wing and the deformation of the membrane structure. In this paper, we introduce a staggered coupling scheme combining a structural finite element solver using a dynamic relaxation technique with a potential flow solver. The developed method proved numerically stable for determining the equilibrium shape of the wing under aerodynamic load and is thus suitable for performance measurement and load estimation. The method was validated with flight data provided by SkySails Power. Measured forces on the tether and steering belt of the robotic kite control pod showed good resemblance with the simulation results. As expected for a potential flow solver, the kite’s glide ratio was overestimated by 10–15%, and the measured tether elevation angle in a neutral flight scenario matched the simulations within 2 degrees. Based on the obtained results, it can be concluded that the proposed aero-structural model can be used for initial designs of ram-air kites with application to airborne wind energy.

A physical model of the simplest three-dimensional tensegrity unit was built at human-scale out of aluminum. Self-stress implementation and static loading tests were performed on this model. At each step, accurate measurements were obtained for all nodal positions and element forces. For the prestressing phase, elongations were imposed, via mechanical devices, in different combinations of elements, called prestress scenarios. Experimental results are compared to the theoretical self-stress state obtained by singular value decomposition of the equilibrium matrix and to numerical simulations using the dynamic relaxation method. It is shown that internal forces follow the same linear trend for all prestress scenarios even if the geometry is significantly impacted. Compressive tests were conducted by hanging masses from the top nodes. It is shown that there exists a unique load-displacement relation, that follows the “infinitesimal” mechanism direction for a “finite” distance which depends on the self-stress level. The paper provides a detailed overview of the simplex’s structural behavior using both experimental and numerical results while discussing the limitations of the analysis methods explored.

Different damage models are proposed in the literature to predict the behavior of dynamic fracture of brittle materials using the peridynamic formulation. The prototype micro-brittle material proposed by Silling and Askari (Comput. Struct. 83:1526−1535, 2005), PMB, and its modified version proposed by Du et al. (J. Elast. 132:197−218, 2018), DTT, concern bond-breakage damage criteria applied to a bond-based constitutive model. These models consider only the direct interaction between material points and have, therefore, a fixed Poisson’s ratio. Lipton et al. (J. Elast. 133:129−153, 2018) propose a state-based peridynamic model, LSJ, which, in addition to the strain state field, also considers a dilatational term and is coupled with a damage criterion that considers failure not only between bonds but also collectively, among all the bonds connected to a given material point. This criterion has two unrelated damage functions, one associated with the strain state field and the other one with its dilatational part only. In this work, we modify the LSJ model to consider only bond-breakage damage, rather than interaction-breakage damage, and call it the LSJ-T model. We also implement a bond-breakage damage criterion in the two-dimensional ordinary, state-based peridynamic model presented by Le et al. (Int. J. Numer. Methods Eng. 98:547−561, 2014), which we call the LPS-T model. In both cases, when the strain state of a bond reaches a critical value, rather than breaking, it is continuously damaged until bond-breakage occurs. To study the capability of these models in simulating the formation and the propagation of cracks, we have simulated numerically the experiment of a thin glass plate with an initial semi-crack under mode I loading. All the models were able to grasp the main features of crack propagation, such as the crack propagation speed and the crack pattern. Both the DTT and the LSJ-T models have predicted symmetric crack paths and no minor branches, which indicate a stable crack propagation path. We have also considered the experiment of a notched cement-mortar plate with a hole under quasi-static mode I loading. This experiment was simulated numerically using the aforementioned damage models together with a dynamic relaxation method. We have obtained solutions of the associated numerical problems, which yield a convergent sequence of response forces in terms of displacements. In addition, crack patterns predicted by these solutions are in good agreement with crack patterns observed experimentally.

An investigation of dynamic behaviors of a sandwich plate containing an imperfect two dimensional functionally graded (2D-FG) core surrounded by two faces on a two-parameter elastic foundation and subjected to a moving load is carried out in this paper. The present sandwich solid is composed of a porous 2D-FG core covered by two homogenous layers. It is assumed that the middle layer has micro voids dispersed uniformly and unevenly through the layer thickness. The fundamental equations are governed within the framework of first-order-shear deformation theory by utilizing Hamilton’s principle, von-Karman geometrical nonlinearity and the principal of mixtures. Newmark direct integration procedure is implemented to transform the dynamic equations into a static form and then the kinetic dynamic relaxation numerical technique in conjunction with the finite difference discretization method are employed to solve the nonlinear partial differential governing equations. Finally, the effects of porosity fraction and scattering patterns, boundary constrains, the variation of materials’ grading indexes and elastic foundation constants on the transient performances of the plate are studied in detail.

Incorporating the arc-length constraint, the dynamic relaxation strategy has been widely used to trace full equilibrium path in the post-buckling analysis of structures. This combined numerical scheme has been shown to be successful for solving snap-through problems, but its applicability to snap-back problems has been rarely investigated and remains unclear. This paper proposes a direct and more general finite-difference equation to investigate the numerical stability of this combined numerical scheme, which is dominated by the spectral radius of amplification matrix. And a key discovery of this paper is that a first minor of the tangent stiffness matrix is always negative once snap back occurs. Due to this negative minor stiffness, the spectral radius is invariably greater than one, resulting in unconditional instability, which demonstrates the invalidity of dynamic relaxation arc-length method for snap-back problems. These important conclusions are corroborated by the numerical results of three representative examples in one-, two- and three-dimensional spaces.

This research presents a new algorithm for the Dynamic Relaxation (DR) method with kinetic damping by utilizing Lagrangian interpolation functions to derive new iterative kinetic DR equations. This...

For tensile membrane structures (TMS), form-finding is the first step in design, in which the structure adopts a unique equilibrium shape based on the initial configuration of the structure and the applied initial prestress. However, the choice of a single robust numerical method for form-finding remains debatable, particularly due to the intensive computation involved. The present work proposes a novel form-finding method for TMS using a swarm intelligence algorithm. Particle swarm optimisation (PSO) is used here as the optimiser in the form-finding analysis, formulated as a (area or potential energy) minimisation problem. The computations involve stochastic PSO runs, until the structure converges to an equilibrium configuration. The proposed form-finding method is demonstrated for two study structures with different optimisation objectives. The proposed PSO-based form-finding technique is found to save significant computation cost, when compared to the most commonly used form-finding algorithm of dynamic relaxation. The PSO-based algorithm is also found to lessen arbitrary parameter selections and to be more robust to the selection of an initial TMS configuration.

In this paper, bending analysis of rectangular functionally graded nanoplates under a uniform transverse load has been considered based on the modified couple stress theory. Using Hamilton’s principle, governing equations are derived based on a higher-order shear deformation theory. The set of coupled equations are solved using the dynamic relaxation method combined with finite difference discretization technique for clamped and simply supported boundary conditions. Finally, the effects of aspect ratio, thickness-to-length ratio, boundary conditions, transverse load, and length scale parameter are studied in detail. The results showed that by rising the length scale-to-thickness ratio, the influence of the grading index on the deflection decreased.

In this article, the buckling of composite plates reinforced with functionally graded distributions of single-walled carbon nanotubes along the thickness direction are studied in the thermal surrou...

Steel arches are widely used to support large span membrane roofs. In order to obtain a lightweight solution, these arches might be formed as a truss. Both the strength of the material and the critical load can limit the load-bearing capacity of the steel arch. Due to the out-of-plane slenderness of a large span arch, it is with utmost importance to utilize the membrane as a restraint against the buckling of the arch. Hence, the investigated structure is supported along a curve in an elastic way, but this support has a highly nonlinear response. The presented analysis of the roof is based on the Dynamic Relaxation Method (DRM). To model the membrane, an 8-node quadrilateral membrane element is used. The truss is modeled by straight bars. To obtain an appropriate model for the out-of-plane behavior of the truss, the flanges of the truss are modeled as sub-trusses: four flange 3D trusses are used to represent the proper stiffness of the real bending resistance of a flange. The truss model fits nicely into the highly nonlinear DRM algorithm of membrane structures. In the equilibrium state of the structure, the classical eigenvalue problem is solved to obtain the critical parameter of the actual load. The elastic and the geometric stiffness of the membrane and respectively the truss elements must be selected to withstand the destabilizing effects safely.

The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers. Because they have highly nonlinear behavior, it is difficult to find solutions to these problems. Thus far, different assumptions and methods have been proposed to solve such structures. The dynamic relaxation method (DRM) is an explicit procedure for analyzing these types of structures. To utilize this scheme, investigators have suggested various stiffness matrices for a cable element. In this study, the efficiency and suitability of six well-known proposed matrices are assessed using the DRM. To achieve this goal, 16 numerical examples and two criteria, namely, the number of iterations and the analysis time, are employed. Based on a comprehensive comparison, the methods are ranked according to the two criteria. The numerical findings clearly reveal the best techniques. Moreover, a variety of benchmark problems are suggested by the authors for future studies of cable structures.

The possibilities of the LOGOS software package for calculating seismic vibrations of buried structures, considering the contact interaction with the ground and the gravity field, are investigated and expanded. To reduce computational costs, the LOGOS software package includes a method for modeling non-reflective boundary conditions that was developed earlier and implemented in the “Dynamics-2” software package, which allows reducing the size of the computational domain. The results of numerical simulation in the LOGOS of shear wave propagation in an elastic bounded subdomain of a continuous medium are presented, demonstrating the effectiveness of non-reflecting boundary conditions for a three-dimensional formulation. The dynamic relaxation technique used in the dynamic strength module of the LOGOS software package for calculating the initial static stresses from the action of the gravity field with the subsequent solution of the non-stationary problem is investigated. Numerical estimates of the expected accuracy of the dynamic solution are obtained, depending on the specified accuracy of the static calculation. Thus, the relative error in the change in kinetic energy when using the dynamic relaxation algorithm 10–4 gives a relative error of 10–3 in velocities and 10–2 in stresses, reducing the specified calculation error by 2 orders of magnitude reduces the relative error in calculating velocities by 3 times, stresses – by 5 times. The calculation of the initial stress-strain state of the building-ground system from the action of the gravity field is compared using the dynamic relaxation procedure and using the stationing procedure implemented in the “Dynamics-2” software package. In all problems in the three-dimensional formulation, 8-node hexahedra with one-point integration are used, in the two-dimensional formulation – equivalent 4-node finite elements, for the integration of the defining system of equations, an explicit “cross” scheme is used. Between the subdomains, variants of contact with gluing and contact with friction are implemented. The capabilities of LOGOS for conducting multiprocessor calculations allowed us to make estimates of the convergence of the problem under consideration based on a series of computational experiments.

Deployable membrane structures such as inflatable stratospheric balloons are known to be sensitive to the occurrence of local instabilities such as wrinkles. The wrinkling phenomenon affects the working performances of the membrane and the occurrence of this phenomenon has to be controlled numerically in order to predict the best means of deployment during the inflation of aerospace balloons. To improve their performances and reliability during flight, the balloons also need to be sized appropriately without the stress field being disturbed by the wrinkles. These instabilities originate numerically from the membrane elements which have a negligible bending stiffness. Several wrinkling models have been presented in the literature in order to solve this problem. However, in most of these models an elastic law and the Green deformation approach have been used for this purpose. The new model called the PS-DPS model presented here for correcting the effects of wrinkles on membrane structures was implemented in the in-house finite element software Herezh++. A projection technique based on a Newton–Raphson method is used to control the stress plane and the in-plane contraction. Using the Almansi strain formulation, this model also accounts for the changes in membrane thickness liable to occur during simulations. The problems due to numerical instabilities are overcome by determining the equilibrium with the so-called Dynamic Relaxation method using kinetic damping procedures. Unlike other membrane models of literature, the PS-DPS model can be used with materials showing complex mechanical behaviour of all kinds. Several benchmark problems are analysed with the present wrinkling model and compared with results available in the literature, focusing first on an elastic law and then on a non-linear hyperelastic law. Lastly, the inflation of a square cushion test and that of a Zero Pressure Balloon are simulated with this non-linear law. The results obtained indicate that the PS-DPS model is valid and accurate to take into account the wrinkles in flexible structures with all these linear and non-linear behaviours.

The paper deals with a neural network to model the flow stress of the AlMg6 alloy at temperatures ranging between 300 and 500 C and strain rates from 1 to 25 s−1. In this temperature–strain-rate range, the movement of free dislocations is blocked and dynamic relaxation processes are inhibited. The results of training the neural network and its verification at a temperature not used in the training show that neural networks with a single hidden layer can correctly approximate and predict the rheological behavior of the AlMg6 alloy for the studied temperature–strain-rate range of deformation.

In future infrared photodetectors, single-walled carbon nanotubes (SWCNTs) are considered as potential candidates due to their band gap, high absorption coefficient (104 - 105 cm −1), high charge carrier mobility and ease of processability. The SWCNT based Field Effect Transistors (CNFETs) are being seriously considered for applications in optoelectronics. In the proposed work optically controlled back gated CNFET is modeled in Sentaurus TCAD to observe the impact of high dielectric oxides on its photoabsorption. The model is based on analytical approximations and parameters extracted from quantum mechanical simulations of the device and depending on the nanotube diameter and the different gate oxide materials. A small deviation in SWCNT chirality shows significant change (more than 50 %) in channel current. Transfer characteristics of the device are analyzed under dark and illuminated conditions. CNFET integrated with HfO2 dielectrics exhibits superior performance with a significant rise in photocurrent current. Precise two dimensional TCAD simulation results and visual figures affirm that the ON state performance of CNFET has significant dependency on the dielectric strength as well as width of the gate oxide and its application in enhancing the performance of carbon nanotube based infrared photo detectors.

In the context of deep rock engineering, the in-situ stress state is of major importance as it plays an important role in rock dynamic response behavior. Thus, stress initialization becomes crucial and is the first step for the dynamic response simulation of rock mass in a high in-situ stress field. In this paper, stress initialization methods, including their principles and operating procedures for reproducing steady in-situ stress state in LS-DYNA, are first introduced. Then the most popular four methods, i.e., explicit dynamic relaxation (DR) method, implicit-explicit sequence method, Dynain file method and quasi-static method, are exemplified through a case analysis by using the RHT and plastic hardening rock material models to simulate rock blasting under in-situ stress condition. Based on the simulations, it is concluded that the stress initialization results obtained by implicit-explicit sequence method and dynain file method are closely related to the rock material model, and the explicit DR method has an obvious advantage in solution time when compared to other methods. Besides that, it is recommended to adopt two separate analyses for the whole numerical simulation of rock mass under the combined action of in-situ stress and dynamic disturbance.

Peridynamics is generally applied to obtain dynamic solutions of crack propagation problems where crack initiation, crack branching and usually fast fracture are involved. A fairly straightforward explicit time-stepping scheme is most commonly used. Quasi-static solutions can be obtained using an adaptive dynamic relaxation method or an energy minimization method applied to the dynamic equations of motion or by solving a linear system of equations in the case of linearized peridynamics for an implicit solution. A direct solution approach by forming a linear system of equations is advantageous as the implementation is fairly straightforward and does not require multiple iterations. However, memory requirements for storing full stiffness matrices scale quadratically with the number of degrees of freedom. For example, in 2D, a grid of nominal size, say 104 particles, would require memory of nearly 3 gigabytes when using double precision. This work presents detailed algorithms that use coordinate and neighbor information to directly generate the sparse matrices required to solve a peridynamic system of equations for quasi-static simulations. The algorithms are first prototyped in MATLAB®; and the stiffness matrix and solutions are verified by comparing with their counterparts obtained by assembling the full stiffness matrix. The algorithms are also implemented in a C++ code that is run on multiple threads and the performance is evaluated as a function of parameters such as problem size, horizon, and the number of threads used. The performance and solutions of two problems with a static crack and a propagating crack are compared with solutions obtained using more traditional methods. It is found that a massive computational gain can be achieved in terms of both memory and performance by taking advantage of multi-threading and sparse implementation simultaneously.

The purpose of the present work is to improve the performance of the standard collaborative optimization (CO) approach based on an existing dynamic relaxation method. This approach may be weakened by starting design points. First, a New Relaxation (NR) method is proposed to solve the difficulties in convergence and low accuracy of CO. The new method is based on the existing dynamic relaxation method and it is achieved by changing the system-level consistency equality constraints into relaxation inequality constraints. Then, a Modified Collaborative Optimization (MCO) approach is proposed to eliminate the impact of the information inconsistency between the system-level and the discipline-level on the feasibility of optimal solutions. In the MCO approach, the impact of the inconsistency is treated by transforming the discipline-level constrained optimization problems into an unconstrained optimization problem using an exact penalty function. Based on the NR method, the performance of the MCO approach carried out by solving two multidisciplinary optimization problems. The obtained results show that the MCO approach has improved the convergence of CO significantly. These results prove that the present MCO succeeds in getting feasible solutions while the CO fails to provide feasible solutions with the used starting design points.

It is shown that, when calculating the trajectories of the motion of polydisperse solid particles in two-phase flows, it is necessary to take into account the time of their dynamic relaxation. A universal dependence of the relaxation time for the particle-deposition rate on its size and density, as well as on the parameters of the dispersion medium, is obtained. An analysis of the relative errors in the approximation of tabular data of the Rayleigh curve by the Adamov and Rosenbaum–Todes formulas, which showed an average approximation deviation of 7–9%, is carried out. New formulas are proposed with optimized empirical coefficients, showing an average relative error of less than 1%. The influence of the velocity of the vertical flow of the medium on the time of dynamic relaxation of solid particles is analyzed. It is noted that, for particles moving in velocity regions close to the speed of their movement, their relaxation time tends to zero. It is proposed for a moving dispersed flow to construct a generalized graph of relative time versus relative speed and, from it, find the time of dynamic relaxation of particles.

A relatively simple technique has been introduced in this paper. The approach is based on the Linear Force Method (FM) with discretion of the applied loads to the subsequence steps and updating coordinates in each iteration to have new geometrical property. The accuracy of the technique depends on the size of the discretion which depends on the number of iterations. A small change in the configuration could hugely affect the displacement and internal forces in geometrically nonlinear structures, that’s why the current approach is vital. The proposed technique is validated with other techniques of nonlinear analysis of the structures with a very good agreement in both terms of external nodal displacements and internal bar forces.

In this paper, we present a 3-dimensional elastic beam model for the form-finding and analysis of elastic gridshells subjected to bending deformation at the self-equilibrium state. Although the axial, bending, and torsional strains of the beam elements are small, the curved beams connected by hinge joints are subjected to large-deformation. The directions and rotation angles of the unit normal vectors at the nodes of the curved surfaces in addition to the translational displacements are chosen as variables. Based on the 3-dimensional elastic beam model, deformation of an element is derived from only the local geometrical relations between the orientations of elements and the unit normal vectors at nodes without resorting to a large rotation formulation in the 3-dimensional space. Deformation of a gridshell with hinge joints is also modeled using the unit normal vectors of the surface. An energy-based formulation is used for deriving the residual forces at the nodes, and the proposed model is implemented within dynamic relaxation method for form-finding and analysis of gridshells. The accuracy of the proposed method using dynamic relaxation method is confirmed in comparison to the results by finite element analysis. The results are also compared with those by optimization approach for minimizing the total potential energy derived using the proposed formulation., This research is partly supported by SPIRITS program 2017 of Kyoto University.

The paper presents a numerical study, within a nonlinear generalization of the classical Ericksen–Leslie theory, of a new nonlinear mechanism for the formation of the regime of shock pressure on the boun-ding walls of a microsized twisted nematic cell (TNC), realized in the form of the kinklike traveling wave $$\mathcal{P}$$(z – $${v}t$$) under the effect of the externally applied electric field and induced by a strong local distribance of the director field in the form of a Gaussian (normal) distribution. The mechanisms responsible for the formation of the traveling wave of shock pressure propagating in the TNC from one of its boundaries to another are studied, and it is shown how the magnitude of the electric field and the shape of the localized initial perturbation of the director field affect the similarity of the traveling wave to the kinklike wave. Studies of the dynamic relaxation of the director field in TNCs also showed that, at temperatures exceeding the temperature for the nematic–smectic A (NA) TNA phase transition by several dozen mK, fluctuations in the order parameter of the emerging smectic phase suppress the effect of the electric field and favor the singular behavior of the azimuthal anchoring energy density as T → TNA.

In this study, a peridynamic model is presented for a Mindlin plate resting on a Winkler elastic foundation. In order to achieve static and quasi-static loading conditions, direct solution of the peridynamic equations is utilised by directly assigning inertia terms to zero rather than using widely adapted adaptive dynamic relaxation approach. The formulation is verified by comparing against a finite element solution for transverse loading condition without considering damage and comparing against a previous study for pure bending of a Mindlin plate with a central crack made of polymethyl methacrylate material having negligibly small elastic foundation stiffness. Finally, the fracture behaviour of a pre-cracked Mindlin plate rested on a Winkler foundation subjected to transverse loading representing a floating ice floe interacting with sloping structures. Similar fracture patterns observed in field observations were successfully captured by peridynamics.

A modified dynamic relaxation algorithm for the form-finding of tensegrity robots in task space is proposed in this paper. There are some form-finding problems of tensegrity structures that are hard to be handled by the node-based dynamic relaxation algorithm. For tensegrity structures with multiple interconnected rods or rigid rods, the node-based dynamic relaxation algorithm is usually difficult to perform this type of form-finding. The node-based dynamic relaxation algorithm becomes rather cumbersome if several different ratios between rod lengths and cable lengths are desired, which restricts its applicability to less regular structural forms. The performance of the algorithm is affected by the relative difference in stiffness between members(cables and rods). To solve these problems, we extend the general dynamic relaxation algorithm from node space to task space. The proposed algorithm considers multiple interconnected rigid rods as an entire rigid body to derive its motion in six degrees of freedom. We simulated the motion process of the rigid body approaching its self-equilibrium position under the force exerted by all surrounding cables. In the form-finding process, the relative location relationship of all interconnected rods on a complex rigid body is maintained. The algorithm is valid for the form-finding of tensegrity structures which are with several different ratios between rod lengths and cable lengths. Besides, the modified algorithm is not affected by the stiffness of interconnected rods on rigid bodies. To demonstrate the capability of the method, four examples, including a two-segment spine robot, a bio-inspired tensegrity arm, a multi-segment spine robot, a tensegrity robot with disconnected and interconnected rigid rods, are presented in this paper.

Dissipative processes in highly elastic latex polymers have been analyzed based on a theoretical calculation of the relaxation microheterogeneity of polymer structures. The microheterogeneity is evaluated graphically from the dependence of the dissipation intensity ratio λ/λmax on the temperature ratio (Т – Тmax)/Тmax. The α-relaxation intensity is determined using the internal friction spectrum recorded by dynamic relaxation spectroscopy.

In this study, interaction of holes in different locations in a tensile loaded composite plate is analysed using Bond-Based Peridynamic (PD) Theory. Moreover, the crack growth behaviour in the plate is investigated. PD simulations are conducted using adaptive dynamic relaxation solution scheme using a code developed in MATLAB. The PD solutions of the crack tip opening displacement is validated with the results obtained through finite element analysis (FEA) using ANSYS. The crack propagation paths and the effect of hole interaction on crack growth behaviour are also investigated using PD theory. Results obtained using PD theory were compared with the results of FEA and Ozaslan et al. (2019). It is found that PD can accurately capture stress, strain and hole interactions in composite laminates.

The airborne wind energy (AWE) technology aims to utilise tethered wings to harvest wind energy at altitudes conventional wind turbines cannot reach. There are two distinct methods to harvest airborne wind energy: onboard and ground-based generation. The onboard generation is achieved through flying fast manoeuvres driving propellers attached to the tethered wing, while the generated electricity is conducted through the tether. On the other hand, the ground-based generation utilises the tether tension of the kite to unwind it from a drum, driving a generator. When the tether is fully extended, it is reeled in by the generator, which consumes energy. Since the traction phase is a lot longer and produces a lot more electricity than electricity needed in the reel-in phase the net energy of such a cycle is positive. SkySails Power is one of the leading companies developing a ground-based AWE generator driven by a large ram-air kite. This thesis describes the development of a methodology for simulating their wing.

The structural performance of any building design is often dependent on the geometrical shape, which affects its behavior and stability. Structural consideration and optimization in the conceptual stage of the design process can lead to better solutions and design exploration. In this paper, a design approach for generating and structurally optimizing the geometrical form in the conceptual design phase is presented. The method is applied to a canopy of an ecological island (waste collection center in Rome, Italy). We demonstrate how parametric structural design can facilitate the decision-maker to generate and analyze the optimal design solutions rapidly in the conceptual stage of the design process. Fully parametric models are created in a Rhinoceros3D® environment and interfaced with in-house built algorithms, and Finite Element simulations are performed in DubalRFEM. An ecological island’s canopy has been completely redesigned with a Genetic Algorithm and a Dynamic Relaxation Algorithm, resulting in a free-form shape-resistant structure. Finally, the shape-optimized canopy meets various requirements (structural, functional, formal) that improve structural efficiency and design collaboration, such as in the role of the architect and engineer in the design process and in the relationship between the designer and design tools.

In some structural systems, such as cable structures, membranes and tensegrity structures, the use of sliding cables allows to reduce the number of elements required to be controlled during tensioning or activation. However, using sliding cables modifies the structural behavior of tensile structures since it alters the distribution of axial forces in structural members. This has been experienced in structures with continuous cables under the assumption of frictionless sliding. However, sliding-induced friction can further alter the behavior of the system. An enhancement of the static analysis of tensile structures with sliding-induced friction is investigated in this paper. In the proposed formulations, the finite-element analysis method and the dynamic relaxation method are combined with a linear complementary approach. Sliding-induced friction is integrated in the formulations through the consideration of the Euler–Eytelwein equation. The importance of considering sliding-induced friction in the static analysis of tensile structures is demonstrated through a series of examples, where it is shown that friction significantly affects the mechanical behavior of the structures. The examples also reveal that the proposed formulations do not affect the computational time of the static analyses.

Low weight and ability to withstand large deformations make tensegrity-based structures attractive for a wide range of applications. It has been reported that given a number of bars (struts), strings (cables) and interconnections between bars and strings, more than one configuration can be arrived at. However, the possibility of taking a tensegrity from one of stable configurations to another has not been reported so far. This paper first explores a Monte Carlo-based method of arriving at different configurations of tensegrity structures having the same number of bars, strings and their interconnections. The results were validated against analytical solutions available in the literature. It then uses the dynamic relaxation method to show the intermediate steps for transforming one configuration into another by the application of a set of external forces. This can lead to multi-usability of tensegrity structures by switching from one stable configuration to other configuration.

The present study aimed to introduce a numerical method to study ratcheting strains of rectangular plates. A new numerical analysis was conducted by development of dynamic relaxation method combined with MATLAB software to evaluate the ratcheting behavior of the thin steel plate under mentioned loading condition. In order to verify the results, experimental tests were performed under stress-controlled conditions by a zwick/roell amsler HB100 machine and bending ratcheting of CK45 steel plate at room temperature was studied. Under stress-controlled conditions with non-zero mean stress, ratcheting behavior occurred on thin plate. Moreover, a finite element analysis was carried out by Abaqus using nonlinear isotropic/kinematic (combined) hardening model. The results showed that the rate of ratcheting strain decreased with an increase in cycle number. It was found that the hysteresis loops were wider in experimental method than those of other methods because of more energy dissipation. The numerical results are in a good agreement with the simulation and experimental data. Comparison of errors between these methods obviously demonstrate high accuracy of the new introduced method.

Dynamic Relaxation Method (DRM) is an explicit approach for solving the simultaneous systems of equations. In this tactic, the fictitious mass and damping are added to the static governing equations, and an artificial dynamic system is constructed. By using DRM for nonlinear analysis, the structural static equilibrium path is obtained. This outcome is extremely valuable, since it leads to the behavior of structures. Among the finding related to the structural static path are the critical and buckling points for nonlinear structures. In this paper, a new way for calculating the load factor is proposed by setting the external work zero. Mixing the dynamic relaxation scheme with external work technique has not been formulated so far. In all incremental-iterative methods, the load factor increment sign should be determinated by extra calculations. This sign leads to increase or decrease of the load increment. It is worth emphasizing that sign of the load factor increment changes at the load limit points. Therefore, the sign determinations are required in the common work control methods. These disadvantages are eliminated in the proposed algorithm. In fact, the suggested load factor depends only on the Dynamic Relaxation (DR) fictitious parameters. Besides, all DR calculations are performed via vector operation. Moreover, the load factor is calculated only by one formula, and it has the same relation in the all solution processes. In contrast to the arc length techniques, which requires the sign determined, the proposed scheme does not need any sign finding. It is shown that author’s technique is quicker than the other dynamic relaxation strategies. To prove the capability and efficiency of the presented scheme, several numerical tests are performed. The results indicate that the suggested approach can trace the complex structural static paths, even in the snap-back and snap-through parts.

Buckling of rods with cylindrical constraints is an essential problem in engineering and medical fields. Completely different to the buckling of classical Euler rods, the post-buckling modes for rods with cylindrical constraints involve highly complicated deformations and geometric configurations. In this paper, the rods are discretized into beam elements by finite element method, and the constraint relation between the rods and cylinders is described by gap element. A dynamic relaxation method for static buckling of compressed rods in cylinders is introduced. Numerical simulations have been carried out to investigate the effects of damping, element length, initial contact stiffness and penetration on post-buckling, etc. The characteristic buckling modes include deflection curves with single point, two points, three points and point-line-point contact. For the helical buckling, it is found that the transition section consists of two noncontact sections only, while the perturbed-helix section does not exist. Except the critical load and shear force of helical buckling, numerical simulation results are in good agreement with the analytical solution. By using the dynamic relaxation method, stable helical buckling modes can be obtained directly without undergoing sinusoidal buckling deformation under given compressive loads.

In this article, a new relationship is proposed for the fictitious mass of viscous dynamic relaxation (DR) method. First, incremental equations are derived for DR steps. Using transformed Gershgori...

Purpose The purpose of this study is to demonstrate that using appropriate values for fictitious parameters is very important in dynamic relation methods. It will be shown that a better scheme can be made by modifying these terms. Design/methodology/approach Former research studies have proposed diverse values for fictitious parameters. These factors are very essential and highly affect structural analyses’ abilities. In this paper, the fictitious masses in ten previous well-known schemes are replaced with each other. These formulations lead to the extra 41 different new procedures. Findings To compare the skills of the created processes with those of the ten previous ones, 14 benchmark problems with geometrical nonlinear behaviour are analysed. The performances’ evaluations are based on the number of iterations and analysis time. Considering these two criteria, the score of each technique is found for the ranking assessments. Research limitations/implications To solve a static problem by using a dynamic relaxation (DR) scheme, it should be first converted to a dynamic space. Using the appropriate values for fictitious terms is very important in this approach. The fictitious mass matrix and damping factor play the most effective role in the process stability. Besides, the fictitious time step is necessary for improving the method convergence rate. Practical implications Different famous DR procedures were compared with each other previously. These solvers used their original assumptions for the imaginary mass and damping. So far, no attempt has been made to change the fictitious parameters of the well-known DR methods. As these fictitious factors highly affect structural analyses’ efficiencies, these solvers are formulated again by using new parameters. In this study, the fictitious masses of ten previous famous methods are replaced with each other. These substitutions give 51 different procedures. Originality/value It is concluded that the present formulations lead to more effective and favourable methods than the solvers with previous assumptions.

cited By 4; International audience; Dynamic relaxation processes are fundamental to understand the mechanical and physical properties of metallic glasses. In the current work, mechanical relaxations in a La 30 Ce 30 Al 15 Co 25 bulk metallic glass were probed by dynamic mechanical analysis. In contrast to many metallic glasses, La 30 Ce 30 Al 15 Co 25 metallic glass shows a pronounced slow β relaxation peak. Physical aging below the glass transition temperature T g leads to an increase of the apparent activation energy and a decrease of the slow β relaxation magnitude. The correlation between the slow β relaxation and the main α relaxation is discussed. © 2019

Molecular dynamics computer simulations are performed to study the structure and dynamic relaxation of the metallic alloys Cu50Ag50 and Cu50Zr50 with and without miscibility gap, respectively. The interactions between the particles are modeled by an effective potential of the modified embedded atom method (MEAM). Cu50Zr50 undercooled liquid shows negative mixing enthalpy; the stronger interaction of heterogeneous atom pairs than that of homogeneous atom pairs, the longer the α-relaxation time and the lower the diffusion coefficient than that of the Cu50Ag50 liquid. Dynamic relaxation is related to the structural heterogeneity: the amount of five-fold symmetry (icosahedron-like) clusters is predominant in Cu50Zr50 melts, which hinders the movement of atoms and increases the dynamic relaxation time. The amount of non-five-fold symmetry (crystal-like) clusters is more pronounced in Cu50Ag50 melts, which leads to shorter dynamic relaxation time and enhanced crystallization of the Cu50Ag50 melt. The quantitative relationship between the five-fold symmetry parameter W and the diffusion coefficient D, as well as the α-relaxation time τ α , is obtained in the two distinct undercooled liquids. The present work provides an understanding of the atomic-scale structure and the dynamic properties in the miscible and immiscible liquid mixtures.

Bending active gridshells are structures that involve sophisticated analysis, design and construction processes. Like shells generally, they can achieve large span to thickness ratios. The computational modelling of bending active gridshells will include, in general, both a form-finding stage and a subsequent stage analysing deformations and internal forces under imposed loads. The analysis of bending active gridshells using the dynamic relaxation method is well represented in the literature. This study examines the effects of different joint models and bracing systems on the stiffness of gridshells. The effect of two types of bracing on stiffness is compared. The effects of different joint models are also examined. The computational modelling is carried out by implementing the dynamic relaxation method in MATLAB and validated by reference to closed form benchmark solutions and previously validated finite element models. Significant variations in stiffness are observed for different bracing and joint models.

There are several statements mentioning the possibilities of combining reciprocal and tensegrity structure. One of those is called reciprocal-tension (rection). This research was aimed to propose rection as a new structural system that also differs from both reciprocal and tensegrity. It defined rection structure and its characteristic, basic configuration and structural behaviour. Three simulations were conducted to test the hypothesis using dynamic relaxation method. The result showed that rection structure had the characteristics of (1) bar under bending stress, that do not touch each other, that hangs to each other reciprocally, and (2) self-equilibrated and pre-stressed system for enough rigidity. The research also concluded that the basic configurations of rection structure consist of upward fan reciprocal and positive double curvature configuration. Structural analysis also had been done on a 1:1 scale experiment and dynamic relaxation simulation.

The effect of low-molecular polysulfones (oligosulfones) on the static and dynamic relaxation properties of epoxy polymers based on industrial resin ED-20 is studied. It is established that the modification of oligosulfones with terminal carboxyl, phenolic groups and a molecular weight from 1200 to 44500 leads to the formation of epoxy systems with higher performance in terms of development of static processes of creep and stress relaxation. It is demonstrated that the dynamic shear modulus increases with the introduction of the modifier. The magnitude of this effect is proportional to the molecular weight of oligosulfones. The intensities of the high-temperature α-transition at 390 K and the low-temperature β-transition at 208 K decrease with the introduction of the modifier. The improvement of the relaxation properties is associated with an increase in the density of the chemical grid of the epoxy matrix with the introduction of modifiers, its saturation with more rigid and heat-resistant component and the formation of additional intermolecular bonds between the components of the system

Cells and tissues exhibit complex mechanical behaviour, including large deformations, migration, growth, cell proliferation and death, as well as changes in behaviour due to external factors (e.g. chemical signals). The discrete element method is well suited for modelling such complicated behaviour, but computational efficiency is difficult to achieve due to the large number of particles needed for discretisation. Most of the mechanical behaviour of cells and tissues takes place slowly enough that it can be considered a quasi-static process. Taking this into account, we developed very efficient algorithms which ensure solution convergence and greatly reduce the computation time; these include an efficient neighbour search algorithm, explicit time integration with dynamic relaxation and stability control using mass scaling. In this paper we describe these algorithms and evaluate their performance using several numerical experiments. We demonstrate how some complex phenomena (constant tension membrane, growth, tissue degradation) can be easily modelled using the proposed methods.

The aim of this article is to assess the speed of convergence of numerical calculation of cable-membrane structures using dynamic relaxation method in the process of finding critical damping pre-calculated on undamped system. The procedure is tested on four different constructions in six numerical cases. The variety of examples is as large as possible to demonstrate the greatest versatility of the test procedure. The efficiency of the procedure is evaluated based on the number of iterations.

This paper presents an estimation method for the static configuration of a steel lazy wave riser (SLWR) using the dynamic relaxation method applied to estimate the configuration of structures with strong geometric non-linearity. The lumped mass model is introduced to reflect the flexible structural characteristics of the riser. In the lumped mass model, the tensions, shear forces, buoyancy, self-weights, and seabed reaction forces at nodal points are considered in order to find the static configuration of the SLWR. The dynamic relaxation method using a viscous damping formulation is applied to the static configuration analysis. Fictitious masses are defined at nodal points using the sum of the largest direct stiffness values of nodal points to ensure the numerical stability. Various case studies were performed according to the bending stiffness and size of the buoyancy module using the dynamic relaxation method. OrcaFlex was employed to validate the accuracy of the developed numerical method.

Shell structures are material efficient structures capable of covering large spans with minimum weight. If concrete is used as the building material for the shell, it must be initially supported by a formwork. These generally rigid formworks, and their supporting falsework structure, are time and material consuming to construct. Recently, researchers have recommended the use of elastic gridshells as falsework system. Unfortunately, the design of such a system is complicated by large deformations of the bending elements. Moreover, since gridshells are inherently flexible, significant displacements generally occur when applying the wet concrete. To overcome these difficulties, this paper presents a design tool to effectively design a gridshell serving as the falsework for a concrete shell. The gridshell is assumed to be constructed from an initially flat grid of straight slender rods, using cables with adjustable lengths to brace the erected gridshell. An optimization algorithm is proposed that fits the shape of the gridshell under the wet concrete loading to a given target shape by manipulating the lengths of the bracing cables. Meanwhile, the optimization algorithm reduces the construction effort by minimizing the number of cables, and the diameter of the grid rods. Moreover, feasibility of the design is ensured by constraining the axial force in the cables and limiting the displacements under increased loading. A gradient-based optimization scheme is adopted, and an implicit dynamic relaxation approach previously developed specifically for the simulation of bending-active structures is used to solve the nonlinear equilibrium equations. Nonlinear effects such as buckling of the grid rods are taken into account by using co-rotational beam elements. The resulting design tool is applied for the design of a scale model, demonstrating the feasibility of the suggested falsework system. The optimized design fits the target better, uses less cables, and is more resistant to additional loading compared to designs from existing design approaches. Comparisons between the numerical and physical models show deviations of up to around 2% of the larger span for the design load and smaller deviations for smaller loads, with differences attributed to small model scaling effects.

When using the explicit dynamic relaxation approach (DRA) to model the quasi-static rock breakage, fragmentation, and flow problems, especially the top-coal caving question, introducing numerical damping into the solution equation is inevitable for reducing the vibration frequency and impact speed of mesh nodes, which is significantly affect the fidelity of the computation results. Although the DRA has been widely adopted to simulate top-coal caving, the reasonable value and calibration method of numerical damping are still open issues. In this study, the calibration process of reasonable numerical damping for modeling top-coal caving is investigated by comparing with the experimental results, in which several geometry parameters of the drawing funnel are selected as the calibration indexes. The result shows that the most reasonable numerical damping value is 0.07 for the numerical modeling of interval top-coal caving in extra-thick coal seams. Finally, the correlation between the numerical damping and the physical top-coal drawing process is discussed. The numerical damping indirectly reflects the fragmentation in multi scale of coal mass and friction interaction between coal particles during the caving process, which reduces the vibration intensity of the top-coal caving system and dissipates the kinetic energy.

Polymer computational simulations enable the prediction of material properties, exploration of the microscopic and macroscopic phenomenon of materials, and guidance of in vitro macromolecular materials design. This paper presents a mesoscopic level, multiscale approach to generate a complex polymer morphology for future simulations of polymer chains aimed at the design of materials or the study of material properties, such as strain/stress relations and electromechanical properties. To generate a complex polymer morphology, a mesoscopic level model is developed, in which the polymer chains are modeled as one-dimensional homogeneous flexible chains, and the crystalline regions are modeled as rigid continuum bodies. The polymer domain is firstly discretized into a uniform mesh. Location, orientation, and size of crystalline regions can be either pre-defined or randomly distributed inside the polymer domain. Nodes of each cuboid element grid located within crystal units are marked as occupied. Then, a random walking process is applied to generate polymer chains. No overlap is permitted between polymer chains nor between polymer chains and crystalline regions. Chain propagation ceases upon reaching the crystal block surface. Polymer chain properties, such as longitudinal stiffness, bending stiffness, and torsional stiffness, are derived based on molecular structures. Interactions, those between polymer chains, and those between polymer chains and crystalline regions are derived based on Lennard-Jones forces. An explicit dynamic relaxation algorism is applied to minimize potential energy. This approach is much more efficient than MD simulation. The computing time required for this mesoscopic simulation is only 0.5-1% of MD simulation. Yet, nanoand micro-scale geometries of polymer morphology can still be analyzed in detail. Polyvinylidene difluoride (PVDF) is selected to demonstrate the efficiency and efficacy of this numerical model due to its high piezoelectric coefficient.

The present paper is devoted to numerical investigation on fracture parameters of cracked shells subjected to out-of-plane loading using ordinary state-based peridynamics (PD). The nonlocal deformation gradient and equivalent domain integral are introduced to evaluate fracture parameters. To reduce the surface effect and obtain more accurate results, the energy method and volume correction algorithm are considered. Meanwhile, the adaptive dynamic relaxation technique is employed to obtain steady-state solutions. From comparisons between PD results and reference solutions, the proposed PD shell model successfully evaluates fracture parameters in both single- and mixed-mode loading conditions.

Common dynamic relaxation (DR) methods use central finite differences to derive fundamental equations. In this study, Lagrangian interpolation functions are utilized to formulate iterative DR relationships with kinetic damping. This procedure leads to an algorithm that, unlike the ubiquitous DR methods, does not require the calculation of nodal velocities thereby marching forward only through successive nodal displacement. Also, the power iteration method is used to determine the optimal time-step ratio. By utilizing this time-step, the restarting analysis phase which is one of the drawbacks of the kinetic DR strategy is eliminated. Furthermore, a new variable load factor is developed based on the concept of minimization of displacement increment function. To evaluate the performance and efficiency of the proposed method, some truss and frame structures with geometrically nonlinear behavior are analyzed. Results prove that the number of convergence iterations and analysis time are reduced in the new kinetic DR scheme in comparison with other conventional DR methods.