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The present article proposes a time‐domain boundary element method (TDBEM) for the three‐dimensional (3D) dissipative wave equation (DWE). Although the fundamental ingredients such as the Green's function for the 3D DWE have been known for a long time, the details of formulation and implementation for such a 3D TDBEM have been unreported yet to the author's best knowledge. The present formulation is performed truly in time domain on the basis of the time‐dependent Green's function and results in a marching‐on‐in‐time fashion. The main concern is in the evaluation of the boundary integrals. For this regard, weakly‐ and removable‐singularities are carefully treated. The proposed TDBEM is checked through the numerical examples whose solutions can be obtained semi‐analytically by means of the inverse Laplace transform. The results of the present TDBEM are satisfactory to validate its formulation and implementation for Neumann problems. On the other hand, the present formulation based on the ordinary boundary integral equation (BIE) is unstable for Dirichlet problems. The numerical analyses for the non‐dissipative case imply that the instability issue can be partially resolved by using the Burton–Miller BIE even in the dissipative case. [ABSTRACT FROM AUTHOR]

The main idea of this work is an application of probabilistic entropy and also relative entropy in the numerical analysis of uncertainty propagation in the homogenization of some composite materials. The homogenization method is based on the determination of deformation energy for the representative volume elements computed with the use of some specific finite element method experiments. Uncertainty propagation concerns material and geometrical design parameters of particulate composites and is performed thanks to an application of polynomial responses; probabilistic moments of the effective tensor are computed via the iterative generalized stochastic perturbation technique and the semi‐analytical probabilistic method. Probabilistic entropy is determined according to Shannon theory, while relative entropies equations employed here follow mathematical models created by Kullback & Leibler, Jeffreys, Hellinger, and Bhattacharyya. Deterministic analyses have been performed with the use of the system ABAQUS, while all the remaining procedures have been programmed in the computer algebra system MAPLE. [ABSTRACT FROM AUTHOR]

A novel explicit time integration method is formulated with sub‐step strategy and Cubic B‐spline interpolation method. Theoretical and numerical analysis are conducted to obtain optimized algorithm properties including algorithm accuracy, spectral stability and numerical dissipation/dispersion. A demonstrative dispersion analysis for wave propagation is presented to acquire optimal algorithm parameter value for finite element analysis of wave propagation problems. Numerical tests demonstrate that new method show desirable algorithm accuracy and convergence for dynamic problems. Especially, for highly nonlinear problems, the new method can provide very accurate and stable solutions. [ABSTRACT FROM AUTHOR]

In this work, a finite‐element formulation for modeling mixed‐mode delamination in layered structures, consisting of two‐node Timoshenko beam finite elements with quadratic linked interpolation and corresponding 4‐node interface elements is presented and compared to a more common approach where linear Lagrange interpolation is used. The principal novelty of the proposed approach is that the vertical displacements of the beam elements, as well as the transversal relative displacements of the interface elements, are interpolated using a quadratic linked interpolation that also takes into account the nodal cross‐sectional rotations of the beam elements. At the same time, the axial displacements and cross‐sectional rotations are interpolated using linear Lagrange polynomials. A bilinear cohesive zone model is embedded in the interface finite elements for delamination modes I and II. Numerical analyses based on the examples from the literature with metal joints show that the formulation with quadratic linked interpolation improves the convergence and robustness of the solution with respect to the approach with linear interpolation. On the other hand, in case of composites with stiff adhesives this formulation exhibits a peculiar behavior with spurious oscillations of the normal interface tractions that leads to a poor performance in mode‐I and mixed‐mode tests. This problem can be easily solved by canceling the quadratic term in the interpolation function and using the standard Lagrange interpolation in such cases. [ABSTRACT FROM AUTHOR]

A numerical limit analysis model for masonry walls subject to in‐plane loading is posed as a discontinuity layout optimization (DLO) problem, with the masonry conveniently modeled using a smeared continuum ("macromodeling") approach and a homogenized yield surface. Unlike finite element limit analysis, DLO is formulated entirely in terms of discontinuities and can produce accurate solutions for problems involving singularities naturally, without the need for mesh refinement. In the homogenized model presented, masonry joints are reduced to interfaces, with sliding governed by an associative friction flow rule and blocks are assumed to be infinitely resistant. The model takes account of the interlock ratio of the masonry blocks, their aspect ratio and the cohesion and coefficient of friction of interfaces in both the vertical and horizontal directions. Results from the proposed model are compared with those from the literature, showing that complex failure mechanisms can be identified and that safe estimates of load carrying capacity can be obtained. Finally, to demonstrate the utility of the proposed modeling approach, it is applied to more complex problems involving interactions with other elements, such as voussoir arches and weak underlying soil layers. [ABSTRACT FROM AUTHOR]

In this article, we present a novel explicit time‐integration algorithm for the coupled hydromechanical soil mechanics problems in a pseudo‐static regime. After introducing the finite element discretization, the semidiscrete ordinary system of equations is integrated explicitly in time with the Runge–Kutta method. It is noted that this formulation is conditionally stable in time. By introducing a stabilization technique, the Polynomial Pressure Projection, and selecting appropriately the stabilization parameter, the formulation becomes unconditionally stable. To illustrate the performance of the method several numerical analysis are reported, considering both elastic and elasto‐plastic soil behavior. [ABSTRACT FROM AUTHOR]

Passive heat sinks cooled by natural convection are reliable, compact, and low‐noise. They are widely used in telecommunication devices, LEDs, and so forth. This work builds upon the recent advancements in fluid topology optimization (TO) to present a case study of two‐ and three‐dimensional optimum design and thermal modeling for the natural convection problems using a reaction–diffusion equation (RDE)‐based level‐set method. To this end, first, a high‐fidelity thermal‐fluid model is constructed where the full Navier–Stokes equations are strongly coupled with the energy equation through the Boussinesq approximation. We benchmark our simulation solver against the experimental analysis and other numerical analysis methods. Next, we carefully investigate the flow behavior under different Grashof numbers using a fully transient simulation solver. Then, we revisit the RDE‐based level‐set TO methodology and construct an open‐source parallel TO framework. The main findings reveal that using the body‐fitted mesh adaptation, the proposed methodology can capture the explicit fluid–solid boundary and we are free of the continuation approach to penalize the design variable to the binary structure. A moderately large‐scale TO problem with 3.56×106 DOFs can be solved in parallel on a standard multi‐process platform. Our numerical implementation uses FreeFEM for finite element analysis, PETSc for distributed linear algebra, and Mmg for mesh adaptation. For comparison and for accessing our various techniques, a variety of 2D and 3D benchmarks are presented to support these remarkable features. [ABSTRACT FROM AUTHOR]

Traditional reliability analysis is based on probability theory with precise distributions. However, determining the distribution of all variables precisely is impossible due to insufficient information. Therefore, random and interval variables may be encountered, and probabilistic reliability methods are hard to use. The existing interval variables make reliability analysis more difficult. In this article, an efficient and robust hybrid reliability analysis method is proposed for structures with both random and interval variables. Firstly, a single‐loop procedure is proposed by performing probabilistic analysis and interval analysis simultaneously in each most probable point search process. Then an improved conjugate sensitivity factor method based on hybrid conjugate gradient direction and adaptive finite step length is developed for probabilistic analysis. Meanwhile, the hybrid conjugate gradient direction together with active set is introduced into the projected gradient method for interval analysis. Finally, a comparison analysis with six numerical examples is provided to validate the performance of the proposed method. The results demonstrate that the proposed method is better than the existing methods in terms of efficiency and robustness for hybrid reliability analysis with random and interval variables. [ABSTRACT FROM AUTHOR]

This article focuses mainly on the development of explicit integration algorithms for structural dynamics. Some known single‐step explicit schemes are first reviewed and their algorithmic parameters are uniformly given as a function of ρb, denoting spectral radius at the bifurcation point. The simple review reveals that there are still some problems to be addressed. Then, a simple but general explicit integration algorithm (GSSE) is presented and analyzed. Besides, a truly self‐starting explicit algorithm and the true explicit form of generalized‐α method are also given. The novel GSSE algorithm possesses very significant advantages in terms of accuracy and dissipation control. The GSSE method achieves not only controllable dissipation at the bifurcation point but also the identical second‐order accuracy of three primary variables. Numerical spectral analysis and examples are provided to clearly show the superiority of novel explicit methods over other single‐step explicit ones. Hence, the novel GSSE method is highly recommended to solving general dynamical problems. [ABSTRACT FROM AUTHOR]

Summary: Numerical analysis of the hyperelastic behavior of polymer materials has drawn significant interest from within the field of mechanical engineering. Currently, hyperelastic models based on the energy density function, such as the Neo‐Hookean, Mooney‐Rivlin, and Ogden models, are used to investigate the hyperelastic responses of materials. Conventionally, constants relating to materials were determined from experimental data by using global least‐squares fitting. However, formulating a constitutive equation to capture the complex behavior of hyperelastic materials was difficult owing to the limitations of the analytical model and experimental data. This study addresses these limitations by using a system of neural networks (NNs) to design a data‐driven surrogate model without a specific function formula, and employs molecular dynamics (MD) simulations to calculate the massive amount of combined loading data of hyperelastic materials. Thus, MD simulations were used to propose an NN constitutive model for hyperelasticity to derive the constitutive equation to model the complex hyperelastic response. In addition, the probability distributions of the numerical solutions of hyperelasticity are used to characterize the uncertainty of the MD models. These statistical finite element results not only present numerical results with reliability ranges but also scattered distributions of the solution obtained from the MD‐based probability distributions. [ABSTRACT FROM AUTHOR]