Some practical procedures for the solution of nonlinear finite element equations

DOI10.1016/0045-7825(80)90051-1zbMath0435.73080OpenAlexW2012274810MaRDI QIDQ1140468

Arthur P. Cimento, Klaus-Jürgen Bathe

Publication date: 1980

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(80)90051-1

zbMATH Keywords

static analysisdynamic analysisimplicit time integrationincremental finite element equationspractical nonlinear analysis

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Dynamical problems in solid mechanics (74H99) Elastic materials (74B99)

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Uses Software

• ADINA

Cites Work

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• Parametric unification of matrix structural analysis: classical formulation and d-connected mixed elements
• Improved solution methods for inelastic rate problems
• On the finite deflections of thin beams
• The solution of nonlinear finite element equations
• New developments in the inelastic analysis of quasistatic and dynamic problems
• Finite element formulations for large deformation dynamic analysis
• Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics
• Adaptive step size selection for use with the continuation method
• Finite-Element Methods for Nonlinear Elastodynamics Which Conserve Energy
• Solution techniques for non−linear finite element problems
• On transient analysis of fluid-structure systems
• The use of ADINA for analysis of mines with explosive fills
• Rank-one and Rank-two Corrections to Positive Definite Matrices Expressed in Product Form
• A version of the Aitken accelerator for computer iteration
• Evaluation of Solution Procedures for Material and/or Geometrically Nonlinear Structural Analysis
• XX.—Studies in Practical Mathematics. II. The Evaluation of the Latent Roots and Latent Vectors of a Matrix