Penetration Analysis of Concrete Plate by 3D FE-SPH Adaptive Coupling Algorithm

Penetration process of concrete plate is simulated by 3D FE-SPH adaptive coupling algorithm, which is based on experimental research of projectile with 25mm diameter penetrates concrete target. In experiment, a high speed camera is used to record dynamic deformation process of concrete plate. Acceleration responses of concrete are obtained by acceleration sensor, which is pre-embedded in target plate. This experiment is also simulated by 3D FE-SPH adaptive coupling algorithm to verify the numerical model. Numerical model is approximated initially by FEM, and distorted elements are automatically converted into meshless particles to simulate damage, splash of concrete by SPH method, when equivalent plastic strain of elements reaches a specified value. Numerical results of damage process and acceleration response of concrete target are in good agreement with the experimental results. And the results show that crack propagation and lateral movement of concrete mainly occur after projectile passing through target. Furthermore, six different models with different geometry sizes are simulated by the coupling algorithm to study on the effects of boundary condition of concrete target.     

An evaluation of equivalent-single-layer and layerwise theories of composite laminates

A review of equivalent-single-layer and layerwise laminate theories is presented and their computational models are discussed. The layerwise theory advanced by the author is reviewed and a variable displacement finite element model and the mesh superposition techniques are described. The variable displacement finite elements contain several different types of assumed displacement fields. By choosing appropriate terms from the multiple displacement field, an entire array of elements with different orders of kinematic refinement can be formed. The variable kinematic finite elements can be conveniently connected together in a single domain for global-local analyses, where the local regions are modeled with refined kinematic elements. In the finite element mesh superposition technique an independent overlay mesh is superimposed on a global mesh to provide localized refinement for regions of interest regardless of the original global mesh topology. Integration of these two ideas yields a very robust and economical computational tool for global-local analysis to determine three-dimensional effects (e.g. stresses) within localized regions of interest in practical laminated composite structures.     

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.     

Parallel point interpolation method for three-dimensional metal forming simulations

Parallel point interpolation method (PIM) is developed for metal forming with large deformation analysis of three-dimensional (3-D) solids, based on the Galerkin weak form formulation using 3-D meshless shape functions constructed using radial basis functions (RBFs). As the radial PIM (RPIM) shape functions have the Kronecker delta functions property, essential boundary conditions can be enforced as easily as in the finite element method (FEM). The kinematics and the explicit integration scheme for PIM meshless method are given. The OpenMP parallelization toolkit is used to parallelize our meshless code, and the parallelization of the PIM meshless code has been conducted for a shared memory system using OpenMP. Some examples are then presented to demonstrate the efficiency and accuracy of the proposed implementations concerning the accuracy and efficiency of the code. It is demonstrated that the present parallel 3-D PIM meshless program is robust, stable, reliable and efficiency for metal forming analysis of 3-D problems.     

A wave finite element‐based formulation for computing the forced response of structures involving rectangular flat shells

The harmonic forced response of structures involving several noncoplanar rectangular flat shells is investigated by using the Wave Finite Element method. Such flat shells are connected along parallel edges where external excitation sources as well as mechanical impedances are likely to occur. Also, they can be connected to one or several coupling elements whose shapes and dynamics can be complex. The dynamic behavior of the connected shells is described by means of numerical wave modes traveling towards and away from the coupling interfaces. Also, the coupling elements are modeled by using the conventional finite element (FE) method. A FE mesh tying procedure between shells having incompatible meshes is considered, which uses Lagrange multipliers for expressing the coupling conditions in wave‐based form. A global wave‐based matrix formulation is proposed for computing the amplitudes of the wave modes traveling along the shells. The resulting displacement solutions are obtained by using a wave mode expansion procedure. The accuracy of the wave‐based matrix formulation is highlighted in comparison with the conventional FE method through three test cases of variable complexities. The relevance of the method for saving large CPU times is emphasized. Its efficiency is also highlighted in comparison with the component mode synthesis technique. Copyright © 2013 John Wiley & Sons, Ltd.     

A three-stage graphics processing unit-based finite element analyses matrix generation strategy for unstructured meshes

With the development of parallel computing architectures, larger and more complex finite element analyses (FEA) are being performed with higher accuracy and smaller execution times. Graphics processing units (GPUs) are one of the major contributors of this computational breakthrough. This work presents a three-stage GPU-based FEA matrix generation strategy with the key idea of decoupling the computation of global matrix indices and values by use of a novel data structure referred to as the neighbor matrix. The first stage computes the neighbor matrix on the GPU based on the unstructured mesh. Using this neighbor matrix, the indices and values of the global matrix are computed separately in the second and third stages. The neighbor matrix is computed for three different element types. Two versions for performing numerical integration and assembly in the same or separate kernels are implemented and simulations are run for different mesh sizes having up to three million degrees of freedom on a single GPU. Comparison with GPU-based parallel implementation from the literature reveals speedup ranging from 4× to 6× for the proposed workload division strategy. Furthermore, the same kernel implementation is found to outperform the separate kernel implementation by 70% to 150% for different element types.     

Enriching the finite element method with meshfree particles in structural mechanics

The automatic generation of meshes for the finite element (FE) method can be an expensive computational burden, especially in structural problems with localized stress peaks. The use of meshless methods can address such an issue, as these techniques do not require the existence of an underlying connection among the particles selected in a general domain. This study advances a numerical strategy that blends the FE method with the meshless local Petrov–Galerkin technique in structural mechanics, with the aim at exploiting the most attractive features of each procedure. The idea relies on the use of FEs to compute a background solution that is locally improved by enriching the approximation space with the basis functions associated to a few meshless points, thus taking advantage of the flexibility ensured by the use of particles disconnected from an underlying grid. Adding the meshless particles only where needed avoids the cost of mesh refining, or even of remeshing, without the prohibitive computational cost of a thoroughly meshfree approach. In the present implementation, an efficient integration strategy for the computation of the coefficients taking into account the mutual FE–meshless local Petrov–Galerkin interactions is introduced. Moreover, essential boundary conditions are enforced separately on both FEs and meshless particles, thus allowing for an overall accuracy improvement also when the enriched region is close to the domain boundary. Numerical examples in structural problems show that the proposed approach can significantly improve the solution accuracy at a local level, with no remeshing effort, and at a low computational cost. Copyright © 2016 John Wiley & Sons, Ltd.     

Enrichment and coupling of the finite element and meshless methods

A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with particles. Thus, there is no need to remesh in adaptive refinement processes. In both cases the same formulation is used, convergence is studied and examples are shown. Copyright © 2000 John Wiley & Sons, Ltd.     

层压玻璃钢板的侵彻阻抗的试验研究

本文给出层压玻璃钢板和钢板的侵彻阻抗的试验研究结果。撞击速度范围为V=600～800m/s,弹丸为钢球。试验结果表明,对于同样的撞击极限速度,层压玻璃钢靶比钢靶约轻(30～40)%。      

A new meshless regular local boundary integral equation (MRLBIE) approach

A new meshless method based on a regular local integral equation and the moving least‐squares approximation is developed. The present method is a truly meshless one as it does not need a ‘finite element or boundary element mesh’, either for purposes of interpolation of the solution variables, or for the integration of the ‘energy’. All integrals can be easily evaluated over regularly shaped domains (in general, spheres in three‐dimensional problems) and their boundaries. No derivatives of the shape functions are needed in constructing the system stiffness matrix for the internal nodes, as well as for those boundary nodes with no essential‐boundary‐condition‐prescribed sections on their local boundaries. Numerical examples presented in the paper show that high rates of convergence with mesh refinement are achievable, and the computational results for the unknown variable and its derivatives are very accurate. No special post‐processing procedure is required to compute the derivatives of the unknown variable, as the original result, from the moving least‐squares approximation, is smooth enough. Copyright © 1999 John Wiley & Sons, Ltd.     

Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method

New enrichment functions are proposed for crack modelling in orthotropic media using the extended finite element method (XFEM). In this method, Heaviside and near‐tip functions are utilized in the framework of the partition of unity method for modelling discontinuities in the classical finite element method. In this procedure, by using meshless based ideas, elements containing a crack are not required to conform to crack edges. Therefore, mesh generation is directly performed ignoring the existence of any crack while the method remains capable of extending the crack without any remeshing requirement. Furthermore, the type of elements around the crack‐tip remains the same as other parts of the finite element model and the number of nodes and consequently degrees of freedom are reduced considerably in comparison to the classical finite element method. Mixed‐mode stress intensity factors (SIFs) are evaluated to determine the fracture properties of domain and to compare the proposed approach with other available methods. In this paper, the interaction integral (M‐integral) is adopted, which is considered as one of the most accurate numerical methods for calculating stress intensity factors. Copyright © 2006 John Wiley & Sons, Ltd.     

The natural radial element method

In this work an innovative numerical approach is proposed, which combines the simplicity of low‐order finite elements connectivity with the geometric flexibility of meshless methods. The natural neighbour concept is applied to enforce the nodal connectivity. Resorting to the Delaunay triangulation a background integration mesh is constructed, completely dependent on the nodal mesh. The nodal connectivity is imposed through nodal sets with reduce size, reducing significantly the test function construction cost. The interpolations functions, constructed using Euclidian norms, are easily obtained. To prove the good behaviour of the proposed interpolation function several data‐fitting examples and first‐order partial differential equations are solved. The proposed numerical method is also extended to the elastostatic analysis, where classic solid mechanics benchmark examples are solved. Copyright © 2013 John Wiley & Sons, Ltd.     

弹体冲击混凝土半无限靶的侵彻阻力与深度计算

假设弹体是刚性的,将弹体侵彻冲击作用下的混凝土靶体划分为粉碎区、径向裂缝弹性区与原始弹性区,并认为侵彻粉碎区域内的混凝土材料处于类似于流体动力学状态,可采用水动力模型.根据伯努利方程推得了细长杆弹侵彻阻抗力的公式,进而求出锥形弹头侵彻阻抗力的等效平面解,得到了弹体的侵彻深度.利用实弹进行了以不同速度侵彻不同强度的混凝土靶体的验证计算,并与多个经验公式做了对比.结果表明,该模型是合理的,与经验公式相比计算结果趋于保守.     

Iterative domain decomposition meshless method modeling of incompressible viscous flows and conjugate heat transfer

We develop an effective domain decomposition meshless methodology for conjugate heat transfer problems modeled by convecting fully viscous incompressible fluid interacting with conducting solids. The meshless formulation for fluid flow modeling is based on a radial basis function interpolation using Hardy inverse Multiquadrics and a time-progression decoupling of the equations using a Helmholtz potential. The domain decomposition approach effectively reduces the conditioning numbers of the resulting algebraic systems, arising from convective and conduction modeling, while increasing efficiency of the solution process and decreasing memory requirements. Moreover, the domain decomposition approach is ideally suited for parallel computation. Numerical examples are presented to validate the approach by comparing the meshless solutions to finite volume method (FVM) solutions provided by a commercial CFD solver.     

Adaptive meshless local maximum-entropy finite element method for convection–diffusion problems

In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection–diffusion problems at various Peclet numbers in both 1D and 2D. By using local maximum-entropy (LME) approximation scheme to construct the element shape functions in the formulation of finite element method (FEM), additional nodes can be introduced within element without any mesh refinement to increase the accuracy of numerical approximation of unknown function, which procedure is similar to conventional p-refinement but without increasing the element connectivity to avoid the high conditioning matrix. The resulted LME-FEM preserves several significant characteristics of conventional FEM such as Kronecker-delta property on element vertices, partition of unity of shape function and exact reproduction of constant and linear functions. Furthermore, according to the essential properties of LME approximation scheme, nodes can be introduced in an arbitrary way and the $C^0$ continuity of the shape function along element edge is kept at the same time. No transition element is needed to connect elements of different orders. The property of arbitrary local refinement makes LME-FEM be a numerical method that can adaptively solve the numerical solutions of various problems where troublesome local mesh refinement is in general necessary to obtain reasonable solutions. Several numerical examples with dramatically varying solutions are presented to test the capability of the current method. The numerical results show that LME-FEM can obtain much better and stable solutions than conventional FEM with linear element.     

Node and element resequencing using the Laplacian of a finite element graph: Part I—General concepts and algorithm

A Finite Element Graph (FEG) is defined here as a nodal graph (G), a dual graph (G*), or a communication graph (G˙) associated with a generic finite element mesh. The Laplacian matrix ( L (G), L (G*) or L (G˙)), used for the study of spectral properties of an FEG, is constructed from usual vertex and edge connectivities of a graph. An automatic algorithm, based on spectral properties of an FEG (G, G* or G˙), is proposed to reorder the nodes and/or elements of the associated finite element mesh. The new algorithm is called Spectral PEG Resequencing (SFR). This algorithm uses global information in the graph, it does not depend on a pseudoperipheral vertex in the resequencing process, and it does not use any kind of level structure of the graph. Moreover, the SFR algorithm is of special advantage in computing environments with vector and parallel processing capabilities. Nodes or elements in the mesh can be reordered depending on the use of an adequate graph representation associated with the mesh. If G is used, then the nodes in the mesh are properly reordered for achieving profile and wavefront reduction of the finite element stiffness matrix. If either G* or G˙ is used, then the elements in the mesh are suitably reordered for a finite element frontai solver, A unified approach involving FEGs and finite element concepts is presented. Conclusions are inferred and possible extensions of this research are pointed out. In Part II of this work,¹ the computational implementation of the SFR algorithm is described and several numerical examples are presented. The examples emphasize important theoretical, numerical and practical aspects of the new resequencing method.     

FINITE ELEMENT ALGORITHMS FOR DYNAMIC SIMULATIONS OF VISCOELASTIC COMPOSITE SHELL STRUCTURES USING CONJUGATED GRADIENT METHOD ON COARSE GRAINED AND MASSIVELY PARALLEL MACHINES

Recently much attention has been paid to high-performance computing and the development of parallel computational strategies and numerical algorithms for large-scale problems. In this present study, a finite element procedure for the dynamic analyses of anisotropic viscoelastic composite shell structures by using degenerated 3-D elements has been studied on vector and coarse grained and massively parallel machines. CRAY hardware performance monitors such as Flowtrace and Perftrace tools are used to obtain performance data for subroutine program modules and specified code segments. The performances of conjugated gradient method, the Cray sparse matrix solver and the Feable solver are evaluated. SIMD and MIMD parallel implementation of the finite element algorithm for dynamic simulation of viscoelastic composite structures on the CM-5 is also presented. The performance studies have been conducted in order to evaluate efficiency of the numerical algorithm on this architecture versus vector processing CRAY systems. Parametric studies on the CM-5 as well as the CRAY system and benchmarks for various problem sizes are shown. The second study is to evaluate how effectively the finite element procedures for viscoelastic composite structures can be solved in the Single Instruction Multiple Data (SIMD) parallel environment. CM-FORTRAN is used. A conjugate gradient method is employed for the solution of systems. In the third study, we propose to implement the finite element algorithm in a scalable distributed parallel environment using a generic message passing library such as PVM. The code is portable to a range of current and future parallel machines. We also introduced the domain decomposition scheme to reduce the communication time. The parallel scalability of the dynamic viscoelastic finite element algorithm in data parallel and scalable distributed parallel environments is also discussed. © 1997 by John Wiley & Sons, Ltd.     

Mesh grading technique using modified isoparametric shape functions and its application to wave propagation problems

Mesh grading of finite element meshes is greatly simplified by allowing two or more finer elements to abut the entire straight or curved edge of a neighbouring coarser element. This paper proposes the technique by which it can be achieved while maintaining inter-element compatibility by introducing modified shape functions. The concepts and potential advantages of this technique are described in detail for two-dimensional isoparametric quadrilateral elements, although the same procedure can also be applied to other element types including three-dimensional. Implementation of this technique to existing finite element programs requires only minimal modifications. Finally, numerical examples are presented to illustrate the application of the mesh grading technique to several wave propagation problems.     

Penetration of a rigid projectile into an elastic-plastic target of finite thickness

This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.     

Gate elements at injection locations in numerical simulations of flow through porous media: applications to mold filling

Mold filling in polymer and composite processing is usually modelled as a special case of Darcy flow in porous media. The flow pattern and the time necessary to fill the mold depend on the ‘gate’ locations where resin is injected into the closed mold. In composite manufacturing, these are commonly outlets of small tubes transporting resin from a reservoir and their diameters are several orders of magnitude smaller than the mold dimensions. Similar size issue is also encountered in other applications of flow through porous media, such as oil and water pumping and drilling. Traditionally, these inlets are modelled by pressure or flow rate boundary condition as applied at a node of the finite element mesh that represents the injection gate. The omission of the inlet radius in the model results in a mathematical singularity as the mesh gets refined. The computed pressure or flow field depends on the mesh size and does not converge to the accurate solution, as the finite element mesh is refined. It is possible to deal with this phenomenon by modelling the inlet geometry more accurately but this approach is inefficient, as it requires additional degrees of freedom and, above all, significantly complicates the modelling process if the inlet location is not fixed a priori. This paper presents a more efficient alternate solution. It uses special ‘gate’ elements embedded in the mesh around the injection locations. Instead of adjusting the geometrical modelling of the injection location, the adjacent elements use modified shape functions to accurately model pressure field in the neighbourhood of small radial inlet. The proper pressure field shape‐functions for ‘gate’ elements based on linear finite elements are derived. The implementation in an existing mold filling simulation and how the ‘gate elements’ are automatically selected is described. An example to demonstrate the use of ‘gate’ elements and convergence towards the accurate solution with mesh refinement is presented. Copyright © 2004 John Wiley & Sons, Ltd.