An integrated approach to solving mechanical problems on parallel computers

Possibilities of a programming environment that integrates the specificity of the different types of parallel computers are presented in the framework of computational structural mechanics. An extension of the development environment of the Finite Element code CASTEM 2000 has been realized to offer the user a global vision on all objects of the parallel application. To facilitate the implementation of parallel applications, this system hides data transfers between processors and allows a direct reuse of modules of the original sequential code. It is an object-based shared virtual memory system which allows a parallelism by data distribution (for non-structured data) or by control distribution; it is therefore well suited to “mechanic” parallelism. To validate this programming environment, domain decomposition techniques well suited to parallel computation have been used.     

An optimisation strategy for industrial metal forming processes

Product improvement and cost reduction have always been important goals in the metal forming industry. The rise of finite element (FEM) simulations for processes has contributed to these goals in a major way. More recently, coupling FEM simulations to mathematical optimisation techniques has shown the potential to make a further giant contribution to product improvement and cost reduction. Much research on the optimisation of metal forming processes has been published during the last couple of years. Although the results are impressive, the optimisation techniques are generally only applicable to specific optimisation problems for specific products and specific metal forming processes. As a consequence, applying optimisation techniques to other metal forming problems requires a lot of optimisation expertise, which forms a barrier for more general industrial application of these techniques. In this paper, we overcome this barrier by proposing a generally applicable optimisation strategy that makes use of FEM simulations of metal forming processes. It consists of a structured methodology for modelling optimisation problems related to metal forming. Subsequently, screening is applied to reduce the size of the optimisation problem by selecting only the most important design variables. Finally, the reduced optimisation problem is solved by an efficient optimisation algorithm. The strategy is generally applicable in a sense that it is not constrained to a certain type of metal forming problem, product or process. Also, any FEM code may be included in the strategy. Furthermore, the structured approach for modelling and solving optimisation problems should enable non-optimisation specialists to apply optimisation techniques to improve their products and processes. The optimisation strategy has been successfully applied to a hydroforming process, which demonstrates the potential of the optimisation of metal forming processes in general and more specific the proposed optimisation strategy.     

Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm

Different numerical optimization strategies were used to find an optimized parameter setting for the sheet metal forming process. A parameterization of a time-dependent blank-holder force was used to control the deep-drawing simulation. Besides the already well-established gradient and direct search algorithms and the response surface method the novel Kriging approach was used as an optimization strategy. Results for two analytical and two sheet metal forming test problems reveal that the new Kriging approach leads to a fast and stable convergence of the optimization process. Parallel simulation is perfectly supported by this method.     

On an automatically parallel generation technique for tetrahedral meshes

A program for the efficient parallel generation of tetrahedral meshes in a wide class of three-dimensional domains having a generalized cylindrical shape is presented. The applied mesh generation strategy is based on the decomposition of some 2D-reference domain into simply connected subdomains. By means of the reference triangulations of these subdomains the tetrahedral layers are built up in parallel. Adaptive grid controlling as well as nodal renumbering algorithms are involved. In the paper several examples are included to demonstrate both the capabilities of the program and the adequate handling with the implemented method of parallelization.     

A robust and accurate geometric model for automated design of drawbeads in sheet metal forming

A robust and accurate geometric model of real drawbeads that can be used for the automated design of drawbeads is presented in the paper. A three-dimensional geometric drawbead is a lofted surface, of which the section curves are constructed parallel to the stamping direction on the control points. Adaptive control point interpolation is introduced to simplify the management of the drawbead geometry and avoid unexpected shapes. Given primitive control points on a drawbead curve, dominant control points are adaptively obtained with the shapes of both the drawbead curve and the binder considered. An a priori heuristic parameter adjustment strategy is proposed to correct the parameter errors of section curves, which improves the accuracy and consistency of the drawbead geometry. By incorporating the proposed geometric drawbead with a previously developed intelligent drawbead optimization algorithm, a fully automated design process for drawbeads is realized that includes geometric modeling, finite element analysis, intelligent optimization of the drawbead geometry, and die manufacturing. Finally, a fender example is presented to verify the feasibility and validity of the fully automated drawbead design process. The simulation results with the optimized geometric drawbeads and equivalent drawbeads are compared with the experimental results. The proposed geometric drawbead shows remarkable practicability and accuracy in the automated design of drawbeads in sheet metal forming and demonstrates good consistency with the experimental results while the equivalent drawbead model introduces unneglectable deviations.     

Tuning the Schur complement computations for finite element partitions

The domain decomposition method (DDM) is an efficient algorithmic tool for the parallelization of finite element computer codes. A variant of the DDM with direct solution algorithm is based on computation of Schur complement matrices for finite element partitions. This paper describes a simple technique that considerably improves execution rate of computationally intensive routines of the Schur complement computations. The technique uses ‘block of columns’ matrix operations and loop unrolling to reduce load instructions from cache memory and to increase instruction-level parallelism. For superscalar RISC processors, experimental results show that it is possible to improve performance of the DDM solution procedure by several times.     

A parallel finite element procedure for contact-impact problems

An efficient parallel finite element procedure for contact-impact problems is presented within the framework of explicit finite element analysis with thepenalty method. The procedure concerned includes a parallel Belytschko-Lin-Tsay shell element generation algorithm and a parallel contact-impact algorithm based on the master-slave slideline algorithm. An element-wise domain decomposition strategy and a communication minimization strategy are featured to achieve almost perfect load balancing among processors and to show scalability of the parallel performance. Throughout this work, a prototype code, named GT-PARADYN, is developed on the IBM SP2 to implement the procedure presented, under message-passing paradigm. Some examples are provided to demonstrate the timing results of the algorithms, discussing the accuracy and efficiency of the code.     

Optimal process design of sheet metal forming for minimum springback via an integrated neural network evolutionary algorithm

The process of sheet metal forming is characterized by various process parameters. Accurate prediction of springback is essential for the design of tools used in sheet metal forming operations. In this paper, an evolutionary algorithm is presented that is capable of handling single/multiobjective, unconstrained and constrained formulations of optimal process design problems. To illustrate the use of the algorithm, a relatively simple springback minimization problem (hemispherical cup-drawing) is solved in this paper, and complete formulations of the algorithm are provided to deal with the constraints and multiple objectives. The algorithm is capable of generating multiple optimal solutions in a single run. The evolutionary algorithm is combined with the finite element method for springback computation, in order to arrive at the set of optimal process parameters. To reduce the computational time required by the evolutionary algorithm due to actual springback computations via the finite element method, a neural network model is developed and integrated within the evolutionary algorithm as an approximator. The results clearly show the viability of the use of the evolutionary algorithm and the use of approximators to derive optimal process parameters for metal forming operations.     

Topology optimization of 2D continua for minimum compliance using parallel computing

Topology optimization is often used in the conceptual design stage as a preprocessing tool to obtain overall material distribution in the solution domain. The resulting topology is then used as an initial guess for shape optimization. It is always desirable to use fine computational grids to obtain high-resolution layouts that minimize the need for shape optimization and postprocessing (Bendsoe and Sigmund, Topology optimization theory, methods and applications. Springer, Berlin Heidelberg New York 2003), but this approach results in high computation cost and is prohibitive for large structures. In the present work, parallel computing in combination with domain decomposition is proposed to reduce the computation time of such problems. The power law approach is used as the material distribution method, and an optimality criteria-based optimizer is used for locating the optimum solution [Sigmund (2001)21:120–127; Rozvany and Olhoff, Topology optimization of structures and composites continua. Kluwer, Norwell 2000]. The equilibrium equations are solved using a preconditioned conjugate gradient algorithm. These calculations have been done using a master–slave programming paradigm on a coarse-grain, multiple instruction multiple data, shared-memory architecture. In this study, by avoiding the assembly of the global stiffness matrix, the memory requirement and computation time has been reduced. The results of the current study show that the parallel computing technique is a valuable tool for solving computationally intensive topology optimization problems.     

基于h型自适应有限元法在薄板冲压成型中的应用

在对薄板冲压成型这一过程进行有限元仿真分析时,难以精确分析场变量发生剧烈变化的应力集中及应变梯度大的区域,如何平衡精度和效率间的关系是冲压成型仿真的关键.因此,基于非线性有限元大变形的相关理论,针对动态仿真的网格自适应关键技术,建立了自适应分析模式下的薄板冲压成型算法.为了提高计算精度,提出基于单元应变能增量的能量误差...     

覆盖件成形缺陷的数值仿真实例分析

为研究汽车大型覆盖件成形规律,并分析其缺陷成因,介绍了板料成形动态显式有限元数值仿真技术的应用现状、基本理论及应用步骤.通过实例研究了采用有限无数值仿真技术进行覆盖件成形缺陷成因仿真分析的途径.仿真结果表明,采用数值仿真可以分析覆盖件变形规律,了解冲压过程中应力、应变分布及方向,成形极限图分布及缺陷情况,进而改进模具结构和冲压工艺,消除成形缺陷、提高产品质量.数值仿真技术是解决大型汽车覆盖件成形缺陷问题的有效工具.     

Dynamics and elasto-dynamics optimization of a 2-DOF planar parallel pick-and-place robot with flexible links

Dynamic modeling and analysis of a 2-DOF translational parallel robot with flexible links for high-speed pick-and-place operation is presented in this paper. Optimization is implemented with the goal to improve the dynamic accuracy of the end-effector at high speed. The governing equations of flexible links within the robot are formulated in the floating reference frame using Euler–Lagrange method, leading to a global FEM model being generated using the KED (Kineto-Elasto-Dynamics) technique. The dynamic characteristics of the robot are then investigated by model analysis. A numerical dynamic index is proposed to identity the range of natural frequency when the robot reaches different configurations. The comparisons are made between the optimized and original designs in terms of dynamic stress and response.     

A parallel multilevel preconditioned iterative pressure Poisson solver for the large-eddy simulation of turbulent flow inside a duct

Turbulent Poiseuille flows inside the square duct are simulated by the large-eddy simulation based on the multilevel Schwarz preconditioned conjugate gradient pressure Poisson solver, which was developed on top of the Portable, Extensible Toolkit for Scientific Computation (PESTc). The impact of the five different matrix reordering techniques for an incomplete LU (ILU) decomposition as a subdomain solver on the overall performance of Schwarz-type preconditioners for the solution of the pressure Poisson equation are studied. The numerical results indicate that ILU of two-level fill-ins with the reverse Cuthill–McKee matrix ordering technique produces the best performance. Further investigation on the parallel performance of different multilevel methods was also conducted for two different problem sizes. It was observed that the computational cost saturates at around six-level for both the problem sizes explored. Also, though the one-level method is better for small problem size, for the larger problem size, the six-level method performs best in terms of scalability and compute time; hence, the benefit of a multilevel method is more obviously.     

Static load balancing applied to Schur complement method

A finite element method often leads to large sparse symmetric and positive definite systems of linear equations. We consider parallel solvers based on the Schur complement method on homogeneous parallel machines with distributed memory. A finite element mesh is partitioned by graph partitioning. Such partitioning results in submeshes with similar numbers of elements and, consequently, submatrices of similar sizes. The submatrices are partially factorised. The time spent on the partial factorisation can be different, i.e., disbalanced, because methods exploiting the sparsity of submatrices are used. This paper proposes a Quality Balancing heuristic that modifies classic mesh partitioning so that the partial factorisation times are balanced, which saves overall computation time, especially for time dependent mechanical and nonstationary transport problems.     

A node-nested Galerkin multigrid method for metal forging simulation

A node-nested Galerkin multigrid method is developed to solve systems provided by mixed formulations of 3D metal forming problems. An algebraic approach is used with operators built on node-nested meshes made of unstructured tetrahedra. The coarse meshes are built by an automatic coarsening algorithm based on node removal and local topological remeshing techniques. This blackbox multigrid preconditioner is developed within the PETSc library. It is plugged to the FORGE3^® finite element software with frequent remeshings. The effectiveness of the resulting multigrid solver is evaluated for several large scale problems with non-linear behaviour, showing very high efficiency. In particular, the linear rate of convergence of the method is verified on various scales simulations.