Implementation of a Direct Procedure for Critical Point Computations

Mäkinen, Jari; Kouhia, Reijo; Fedoroff, Alexis; Marjamäki, Heikki

doi:10.4203/ccp.93.152

Cited by 1 publication

(2 citation statements)

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“…The procedure is independent of element formulations, if capable to handle large incremental displacements and rotations. Similar results as presented here have been obtained also for solid elements, see Reference . Further developments will be focused on enlarging the convergence domain to improve the robustness.…”

Section: Discussionsupporting

confidence: 86%

“…Solution of the augmented system by the block elimination method requires factorization of one matrix of order n , reductions and back‐substitutions of 2(1 + p ) RHS‐vectors. An alternative scheme suitable for the use of iterative linear solvers is described in , which operates directly with , but the preconditioner is set up in a block form and the incomplete factorization (or some other preconditioner) need to be computed only for the standard stiffness matrix.…”

Section: Determination Of Critical Pointsmentioning

confidence: 99%

See 1 more Smart Citation

Direct computation of critical equilibrium states for spatial beams and frames

Mäkinen

Kouhia

Fedoroff

et al. 2011

Numerical Meth Engineering

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SUMMARYIn this paper, explicit formulas for second order derivatives of the residual vector with respect to the state variables for a geometrically exact 3D beam element based on the Reissner's model are presented. These derivatives are required when a direct non-linear stability eigenvalue problem is solved by the Newton's method. If the external load is parametrized by a single parameter, such an eigenvalue problem consists of solving the critical state variables, the eigenmode, and the critical load parameter from the equation system consisting of the equilibrium equations, the criticality condition, and some auxiliary conditions depending on the type of a critical point.

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Section: Discussionsupporting

confidence: 86%

Section: Determination Of Critical Pointsmentioning

confidence: 99%