English / Japanese
Member:Hirohisa NOGUCHI (Keio Univ.) Tomoshi MIYAMURA (Univ. of Tokyo)
The final objective of this subproject is to develop a general-purpose nonlinear FEM code which can analyze solids and structures of arbitrary shapes with 10 million dofs. The code will be implemented on the massively parallel processors with 30-100 TFlops which will be available in 2002.
A prototype of the code is being developed. Elastic-plastic problem with one million dofs will be analized. In this year the analysis is limited to infinitesimal deformation static analysis.
Domain decomposition method is used for an algorithm of parallel computing. In elastic-plastic analysis, the backward Euler integration scheme is employed for stress integration. The consistent tangent stress-strain relation is used in Newton-Raphson method for the equilibrium iteration.
In the domain decomposition method (abbreviated as DDM), an analysis domain is subdivided in subdomains. The subdomains are solved by a direct solver and dofs at interfaces of subdomains are solved by an iterative solver such as the conjugate gradient method.
Data of subdomains are in memories of 'father' processor(s). They are allocated dynamically to 'child' processors. In the 'child' processors the dofs of inner nodes of each subdomain is eliminated by using the skyline method. The dofs of displacements at the interfaces of subdomains are updated by using the CG method in the 'father' processor(s). Parallel analyses at the subdomain level are carried out in each iteration of CG method. Because no communication among the subdomains is needed, dynamic workload balancing is easily achieved.
When large scale problems are analized, more than one processor is necessary as 'father' processor. In this case a 'grand father' processor manages the 'father' and 'child' processors.
Elastic predictor-radial return method is adopted as stress integration scheme. In this method the incremental plastic strains are calculated by integrating the flow rule with the use of the backward Euler integration technique. Investigations by many researchers show that acceptable solutions are obtained by this method even with large incremental steps. Exact solution is obtained if the direction of the deviatoric stress vector does not change.
The tangent stress-strain matrix which is consistent with the stress integration by the elastic predictor-radial return method is employed in calculating the tangent stiffness matrix. Quadratic convergence in the Newton-Raphson method for the equilibrium iteration can be achieved when the 'consistent' tangent stiffness matrix is used.
Plastic instability analysis, Buckling analysis, Bifurcation analysis, Post buckling analysis using arc-length method, sensitivity analysis etc.
Tomoshi MIYAMURA (miyamura@garlic.q.t.u-tokyo.ac.jp)
Hirohisa NOGUCHI (noguchi@sd.keio.ac.jp)
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Last modified on March 4th, 1998