Finite element analysis of strip rolling process using distributive parallel algorithm

A parallel approach using a network of engineering workstations is presented for the efficient computation in the elastoplastic analysis of strip rolling process. The domain decomposition method coupled with the frontal solver for elimination of internal degrees of freedom in each subdomain is used. PVM is used for message passing and synchronization between processors. A 2-D plane strain problem and the strip rolling process are analyzed to demonstrate the performance of the algorithm and factors that have a great effect on efficiency are discussed. In spite of much communication time on the network the result illustrates the advantages of this parallel algorithm over its corresponding sequential algorithm

The Least-Squares Meshfree Method for the Analysis of Rigid-Plastic Deformation

The least-squares formulation for rigid-plasticity based on J2-flow rule and infinitesimal theory and its meshfree implementation using moving least-squares approximation are proposed. In the least-squares formulation the squared residuals of the constitutive and equilibrium equations are minimized. Those residuals are represented in a form of first-order differential system using the velocity and stress components as independent variables. For the enforcement of the boundary and frictional contact conditions, penalty scheme is employed. Also the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near the contact interface. The proposed least-squares meshfree method does not require any structure of extrinsic cells during the whole process of analysis. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are investigated

A Study on the Adaptive Scheme Using Least-Squares Meshfree Method

An h-adaptive scheme of first-order least-squares meshfree method is presented. A posteriori error estimates, which can be readily computed from the residual, are also presented. For elliptic problem the error indicators are further improved by applying the Aubin-Nitsche method. In the proposed refinement scheme, Voronoi cells are utilized to insert nodes at appropriate positions. Through numerical examples, it is demonstrated that the error indicators reveal good correlations with the actual errors and the adaptive first-order least-squares meshfree method is effectively applied to the localized problems such as the shock formation in fluid dynamics

The Meshfree Method Based on the Least-Squares Formulation for Elasto-Plasticity

A new meshfree method for the analysis of elasto-plastic deformations is presented. The method is based on the proposed first-order least-squares formulation, to which the moving least-squares approximation is applied. The least-squares formulation for the classical elasto-plasticity and its extension to an incrementally objective formulation for finite deformations are proposed. In the formulation, the equilibrium equation and flow rule are enforced in least-squares sense, while the hardening law and loading/unloading condition are enforced exactly at each integration point. The closest point projection method for the integration of rate-form constitutive equation is inherently involved in the formulation, and thus the radial-return mapping algorithm is not performed explicitly. Also the penalty schemes for the enforcement of the boundary and frictional contact conditions are devised. The main benefit of the proposed method is that any structure of cells is not used during the whole process of analysis. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are presented

Finite Element Analysis of Shape Rolling Process using Destributive Parallel Algorithms on Cray T3E

Parallel Approaches using Cray T3E which is NIPP (Massively Parallel Processors) machine are presented for the efficient computation of the finite element analysis of 3-D shape rolling processes. D omain decomposition method coupled with parallel linear equation solver is used. Domain decomposition is applied for obtaining element tangent stifffiess matrices and residual vectors. Direct and iterative parallel algorithms are used for solving the linear equations. Direct algorithm is_parallel version of direct banded matrix solver. For iterative algorithms, the well-known preconditioned conjugate gradient solver with Jacobi preconditioner is also employed. Moreover a new effective iterative scheme with block inverse matrix preconditioner, which is named by present authors, is presented and its results are compared with the one using Jacobi preconditioner. PVM and MPI are used for message passing and synchronization between processors. The performance and efficiency of each algorithm is discussed and comparisons are made among different algorithms

Finite element analysis of strip rolling process using distributive parallel algorithm

학위논문(석사) - 한국과학기술원 : 기계공학과, 1997.2, [ viii, 74 p. ]한국과학기술원 : 기계공학과

최소 제곱 무요소법을 이용한 탄소성 변형 해석에 관한 연구

학위논문(박사) - 한국과학기술원 : 기계공학전공, 2004.2, [ xi, 192 p. ]The least-squares meshfree methods for the linear elasticity, rigid-plasticity and elasto-plasticity are presented. The methods are based on the proposed first-order least-squares formulations and the moving least-squares approximation. The main benefit of the proposed methods is the full achievement of meshfree strategy for the numerical analysis of the problems in solid mechanics. To be a truly meshfree method, the approximation, the domain integration of variational formulation, the treatment of incompressible locking and the remodeling could be performed without any structure of mesh. The proposed methods satisfy these demands. Despite the recent development of the meshfree approximations such as the moving least-squares or reproducing kernel approximations, their applications to the Galerkin formulation require accurate integration for which element-like cells are often employed. Recently, it has been shown that the least-squares formulation is robust to integration errors. Thus a simple or cell-free integration scheme can be effectively used. For this purpose, the support integration scheme, where the integration points are distributed within nodal supports, is presented in the present work. First, the least-squares meshfree method is applied to the linear elasticity. For this, two first-order least-squares formulations, the conventional and compatibility-imposed formulations, are presented. Both formulations achieve the solution accuracy comparable to that of Galerkin formulation. The compatibility-imposed formulation shows the optimal rate of convergence for both primal and dual variables. It is also shown that the least-squares meshfree methods work well with cell-free integration schemes. Another merit of the least-squares method is its uniform convergence behavior in the incompressible condition with equal-order shape functions for both primal and dual variables. The mixed Galerkin method requires lower-order approximation for dual variables, and ...한국과학기술원 : 기계공학전공