Explicit Finite Element Algorithm Research Articles

Large‐scale seismic soil–structure interaction analysis via efficient finite element modeling and multi‐GPU parallel explicit algorithm

AbstractAs urban population increases, integrated underground–aboveground complexes are being constructed at growing paces in major cities. The seismic analysis of such complexes is crucial for the safety and functionality in the threat of potential earthquake disasters. However, fine‐grained numerical modeling and analysis of such large and complex structures are still inefficient due to the consideration of the soil–structure interaction (SSI). To address this challenge, an efficient approach for numerical modeling of large‐scale seismic SSI analysis is presented in this paper to overcome the limitations of existing finite element analysis (FEA) software. Moreover, a multi‐graphic processing unit (GPU) parallel explicit algorithm is implemented for the nonlinear dynamic SSI problems to further increase the computational efficiency. A large underground–aboveground complex project in China is used as an example to demonstrate the capability of the integrated method. The accuracy and reliability of the multi‐GPU parallel explicit finite element algorithm for SSI analysis (GFEA‐SSIA) are verified through a comparative analysis of the linear‐elastic and nonlinear dynamic response of the building calculated by GFEA‐SSIA and common FEA software. Finally, the structural response and structural damage of the underground–aboveground complex are analyzed under multidirectional seismic motions, and the damage distributions of the structures are provided.

Crash Box Impact Energy Absorption

Abstract: Crashworthiness parameters like internal energy absorption and crush force efficiency are the key constants in evaluating the component crashworthiness and its safety in the design of automotive structures for crashworthiness, there is an immense requirement for null strain sub modules that provide a rigid room of survival area for the occupants and deformable sub modules. Which can dematerialize the kinetic energy effectively? The front crash box of an automotive car is one of the most important deformable components which dissipate kinetic energy while frontal crash, which is the most persistent crash situation, affects the entire automotive structural behavior. In this research, quasi-static axial loading response and crashworthiness characteristics of empty hollow tube have been investigated through experimental and numerical simulations. The axial quasi-static loading was executed at a feed rate to evaluate the crashworthiness constants of each sample against quasi-static loading. The supremacy of feed rate empty hallow structures were pursued. The numerical simulation of quasi-static test was performed in accordance with explicit finite element algorithm of LS-DYNA in order to investigate and justify the crashworthiness of each variety of specimens with experimental results.

Wave propagation in thermo-poroelasticity: A finite-element approach

We have developed continuous and discrete-time finite-element (FE) methods to solve an initial boundary-value problem for the thermo-poroelasticity wave equation based on the combined Biot/Lord-Shulman (LS) theories to describe the porous and thermal effects, respectively. In particular, the LS model, which includes a Maxwell-Vernotte-Cattaneo relaxation term, leads to a hyperbolic heat equation, thus avoiding infinite signal velocities. The FE methods are formulated on a bounded domain with absorbing boundary conditions at the artificial boundaries. The dynamical equations predict four propagation modes, a fast P (P1) wave, a Biot slow (P2) wave, a thermal (T) wave, and a shear (S) wave. The spatial discretization uses globally continuous bilinear polynomials to represent solid displacements and temperature, whereas the vector part of the Raviart-Thomas-Nedelec of zero order is used to represent fluid displacements. First, a priori optimal error estimates are derived for the continuous-time FE method, and then an explicit conditionally stable discrete-time FE method is defined and analyzed. The explicit FE algorithm is implemented in one dimension to analyze the behavior of the P1, P2, and T waves. The algorithms can be useful for a better understanding of seismic waves in hydrocarbon reservoirs and crustal rocks, whose description is mainly based on the assumption of isothermal wave propagation.

An unconditionally stable explicit finite element algorithm for coupled hydromechanical problems of soil mechanics in pseudo‐static conditions

AbstractIn 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.

A Penalty Function Method for Modelling Frictional Contact in MPM

Frictional contact is commonly represented in the Material Point Method (MPM) by algorithms based on multi-velocity fields, in which the correction is performed at the background computational mesh. Typically for applications of various stiffness values, these algorithms show a non-physical variation in the contact stresses along the interface surface. The lack of a smoothening function in the detection procedure, which is essential in explicit finite element algorithms, contributes to the stress oscillation and causes a gap between the bodies in contact. For MPM versions with a finite particle size, like Convected Particle Domain Interpolation method (CPDI), the effect of the last shortcoming becomes more pronounced. Results can be improved by using denser mesh, however, the computational cost will increase considerably.In the present paper, the boundary of a continuum object is discretised separately from the MPM discretisation and traced accurately during the solution advancement. Therefore, contact forces among different boundaries are evaluated using a penalty function method commonly implemented in Lagrangian analyses. These forces are then mapped to the computational mesh, where the momentum equation is solved, as an external force. The suggested approach is validated with a benchmark problem, where the closed-form solution is available, and compared to the classical MPM contact algorithm. Furthermore, an application of two bodies collision with large deformation is demonstrated.

Study on Collapse Numerical Simulation Method of Frame Structures Based on Explicit Dynamics

According to the theory of collapse numerical simulation, the explicit finite element algorithm based on explicit dynamics was chose as the numerical calculation method. And combined with the plane RC frame collapse test and the example of ten layers frame structure, the wire frame model, integrated model and separate model were established and the alternate path method was adopted to study the simulate method of structural collapse. With the comparison of several aspects to the results, the rationality of the numerical simulation method and the applicability of the numerical models were verified respectively. At the same time, according to the complex pre-treatment process to the numerical simulation of structural collapse, an MFC program with the function of exporting APDL file which can generate wireframe models for structural collapse simulation in ANSYS/LS-DYNA was developed using VC++ language with the purpose of offering convenience to the numerical simulation process of structure collapse.

Finite element simulations of dynamics of multivariant martensitic phase transitions based on Ginzburg–Landau theory

A finite element approach is suggested for the modeling of multivariant stress-induced martensitic phase transitions (PTs) in elastic materials at the nanoscale for the 2-D and 3-D cases, for quasi-static and dynamic formulations. The approach is based on the phase-field theory, which includes the Ginzburg–Landau equations with an advanced thermodynamic potential that captures the main features of macroscopic stress–strain curves. The model consists of a coupled system of the Ginzburg–Landau equations and the static or dynamic elasticity equations, and it describes evolution of distributions of austenite and different martensitic variants in terms of corresponding order parameters. The suggested explicit finite element algorithm allows decoupling of the Ginzburg–Landau and elasticity equations for small time increments. Based on the developed phase-field approach, the simulation of the microstructure evolution for cubic-tetragonal martensitic PT in a NiAl alloy is presented for quasi-statics (i.e., without inertial forces) and dynamic formulations in the 2-D and 3-D cases. The numerical results show the significant influence of inertial effects on microstructure evolution in single- and polycrystalline samples, even for the traditional problem of relaxation of initial perturbations to stationary microstructure.

Numerical Investigation on the Structural Behavior of a Composite Impact Absorber

The energy absorption capability of an exposed crashworthy element or system is largely affected by material properties and structural design: prismatic sandwich structures, made of foam or honeycomb core between two metallic or laminated composite face plates, are good candidates. This work deals with a numerical investigation on the energy absorbing capability of such a structural component. There are several difficulties associated with the numerical simulation of a composite impact-absorber, such as high geometrical non-linearities, boundary contact conditions, failure criteria, material behaviour; that is because the main objectives of any numerical investigation are the calibration of the model with experimental results and the evaluation of the sensitivity of the variables with respect to the geometrical and physical parameters which influence the study at hand. The latter is a very relevant aspect for designers if the application of the model to real cases has to be a robust one from both a physical and a numerical point of view. In this paper a preliminary calibration of a numerical model for a composite impact absorber is presented, on the basis of experimental data found in literature; then a sensitivity analysis of the same model to the variation of the main geometrical and material parameters, developed by using the explicit finite element algorithms implemented in the Ls-Dyna code, is illustrated.

A Study of the Effect of Infilled Brick Walls on Behavior of Eccentrically Braced Frames Using Explicit Finite Elements Method

Problem statement: Eccentrically Braced Frames (EBFs) are usually infilled by masonry walls, but in common design, the stiffness and lateral resistance of these walls is ignored. Considering the results of carried out tests and studies, it seems that infilled masonry walls have a significant influence on the stiffness and the strength of EBFs. Since experimental test of total frame with infilled brick wall is a very expensive and time consuming process, proper numerical models which can precisely simulate the behavior of EBFs considering the effects of infilled brick wall are necessary. Approach: In this study, a proper model is made using explicit finite elements method to study the behavior of EBFs with infilled masonry wall. Because of complicated mechanical and geometrical properties of masonry walls and also because of the interaction between steel frame and masonry wall, this model is not easy to obtain. To ensure the ability of the model to precisely simulate the behavior of an EBF with infilled brick wall, initial models were made and the problems were solved comparing the results of experimental test and the results of these initial models. Firstly, material models and some basic principles of explicit finite element algorithm are used and three initial models were made: a model of a brick wall without eccentrically braced steel frame, a model of an EBF without infilled brick wall and finally a model of an EBF with infilled brick wall. Results: Using these three initial models, constitutive model for masonry and steel material and also the proper elements for modeling the behavior of mortar is obtained. Studies showed that good prediction of the behavior of a system consisting of EBF and masonry wall is possible, by minimizing the kinematical energy and using a special time scaling of explicit finite element model. Conclusion: After verifying the finite element models, the influence of masonry infilled wall on the behavior of eccentrically braced frames is studied. This investigation showed that in general, the presence of masonry wall increases the yield strength and the elastic range in the force-displacement curves. But the plastic behavior of the frame is deteriorated and due to fragile behavior of masonry materials, the total system of steel frame and masonry wall has a significant strength fall when the elastic range is passed.

Explicit finite element analysis of lightly reinforced masonry shear walls

Explicit finite element analysis (FEA) of masonry shear walls containing reinforcement at spacing between 800 mm and 2000 mm, referred to as wide spaced reinforced masonry (WSRM), are modelled using macroscopic material characteristics for the unreinforced masonry (URM) panels and damaged concrete plasticity for the grouted cores containing reinforcement. The material model and some basic principles of the explicit finite element algorithm are briefly discussed. It has been shown that by minimising the kinetic energy and using an appropriate time scaling and/or damping factor, the FEA could provide reasonable and efficient prediction of the behaviour of the WSRM and URM shear walls.

Nonuniform prestress from prior earthquakes and the effect on dynamics of branched fault systems

To examine the effects of branched fault geometry on the dynamics of fault systems in the long term, we perform multicycle simulations on generic faulting models. An explicit finite element algorithm is used to simulate spontaneous dynamic rupture of earthquakes. The fault stress during the interseismic period is evaluated by an analytical viscoelastic model. We find that the fault prestress field becomes highly nonuniform near the branch point and on the two branch segments over multiple earthquake cycles, owing to the branched fault geometry and stress interaction between the two segments. The principal prestress on faults rotates over multiple earthquake cycles and departs from the regional stress field significantly near the branch point. After a number of earthquake cycles, the branched fault systems evolve to a steady state in which several patterns of the fault prestress and earthquake rupture repeat. The nonuniform prestress developed from previous earthquakes has large effects on the rupture and slip patterns. Several different rupture scenarios can occur on a given branched fault system. In addition, backward branching can occur in the nonuniform prestress field, either driven by slip on the “stem” of the fault system or through a triggering mechanism. These modeling results may have important implications for understanding fault‐branching behavior observed in the 1992 Landers, the 1999 Hector Mine, and the 2002 Denali fault earthquakes and for seismic hazard analysis in the areas where branched fault systems exist.

An explicit finite element algorithm for convection heat transfer problems

A finite element algorithm is presented for the simulation of steady incompressible fluid flow with heat transfer using triangular meshes. The continuity equation is modified by employing the artificial compressibility concept to provide coupling between the pressure and velocity fields of the fluid. A standard Galerkin finite element method is used for spatial discretization and an explicit multistage Runge‐Kutta scheme is used to march in the time domain. The resulting procedure is stabilized using an artificial dissipation technique. To demonstrate the performance of the proposed algorithm a wide range of test cases is solved including applications with and without heat transfer. Both natural and forced convection applications are studied.

Adaptive quadrilateral and triangular finite-element scheme for compressible flows

The development of an adaptive mesh refinement procedure for analyzing high-speed compressible flows using the finite-element method is described. This new adaptation procedure, which uses both quadrilateral and triangular elements, was implemented with two explicit finite-element algorithms - the two-step Taylor-Galerkin and the multistep Galerkin-Runge-Kutta schemes. A von Neumann stability analysis and a rotating 'cosine hill'problem demonstrate the instability of the Taylor-Galerkin scheme when coupled with the adaptation procedure. For the same adaptive refinement scheme, the Galerkin-Runge-Kutta procedure yields stable solutions within its explicit stability limit. The utility of this new adaptation procedure for the prediction of compressible flow features is illustrated for inviscid problems involving strong shock interactions at hypersonic speeds.

An operator‐splitting algorithm for two‐dimensional convection–dispersion–reaction problems

AbstractAn operator‐splitting algorithm for the two‐dimensional convection–dispersion–reaction equation is developed. The flow domain is discretized into triangular elements which are fixed in time. The governing equation is split into three successive initial value problems: a pure convection problem, a pure dispersion problem and a pure reaction problem. For the pure convection problem, solutions are found by the method of characteristics. The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point. A cubic polynomial is used to interpolate the concentration and its derivatives on an element. For the pure dispersion problem, an explicit finite element algorithm is employed. Analytical solutions are obtained for the pure reaction problem. The treatment of the boundary conditions is also discussed. Several numerical examples are presented. Numerical results agree well with analytical solutions. Because cubic polynomials are used in the interpolation, very little numerical damping and oscillation are introduced, even for the pure convection problem.

A numerical analysis of freezing and melting with convection

Abstract An explicit finite element algorithm is presented for the solution of the basic equations describing combined conductive and convective transfer of heat in materials which may undergo a liquid/solid change of phase. The method is used to analyse the influence of natural convection on the process of freezing and melting in a cylindrical thermal cavity. The results produced in the case of freezing are shown to agree qualitatively with experimental observations.