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A Moore–Penrose continuation method based on a Schur complement approach for nonlinear finite element bifurcation problems

https://doi.org/10.1016/j.compstruc.2015.02.003
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Mixed Finite Element Methods and Applications
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Une méthode numérique pour les problèmes d'équilibre de corps hyperélastiques compressibles en grandes déformations
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Approximation of incompressible large deformation elastic problems: some unresolved issues
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Analysis of postbuckling behavior of line pipe subjected to combined loads
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Consistent linearization for path following methods in nonlinear fe analysis
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Numerical analysis of continuation methods for nonlinear structural problems
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On the automatic solution of nonlinear finite element equations
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Finite element analysis of plane strain bifurcation within compressible solids
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An efficient algorithm for the determination of certain bifurcation points
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A stability study of some mixed finite elements for large deformation elasticity problems
inferredcites →https://doi.org/10.1016/j.compstruc.2010.02.007openalex-snapshot
Comparison of the performance of some finite element discretizations for large deformation elasticity problems
inferredcites →https://doi.org/10.1016/j.ijsolstr.2006.10.012openalex-snapshot
Post-bifurcation equilibria in the plane-strain test of a hyperelastic rectangular block
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Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids
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A boundary element technique for incremental, non-linear elasticity
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MATRIX-FREE NUMERICAL CONTINUATION AND BIFURCATION*
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A simple method for the calculation of postcritical branches
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The Application of Newton’s Method to the Problem of Elastic Stability
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Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
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Iterative Methods for Sparse Linear Systems
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Introduction to Numerical Continuation Methods
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MATCONT
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Applicability of Finite Element Method to Collapse Analysis of Steel Connection under Compression
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Numerical Continuation Methods--An Introduction.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations
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Study on the chaotic dynamics in yaw–pitch–roll coupling of asymmetric rolling projectiles with nonlinear aerodynamics
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Parallel numerical continuation of periodic responses of local nonlinear systems
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Periodic solution and stability analysis of dry friction system based on an alternate state-space shooting algorithm
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Harmonic balance method integrated with a customized state-space algorithm for the periodic solutions of structures with frictional hysteresis
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Improved algorithm for the detection of bifurcation points in nonlinear finite element problems
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Improved Moore-Penrose continuation algorithm for the computation of problems with critical points
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Predicting bifurcations in Moore–Penrose continuation using a CNN–LSTM model
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A Time-Domain Spectral Finite Element Method for Acoustoelasticity: Modeling the Effect of Mechanical Loading on Guided Wave Propagation
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Adaptive Homotopy Continuation Using Reinforcement Learning for Enhanced Convergence and Computational Efficiency
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Adaptive Homotopy Continuation Using Reinforcement Learning for Enhanced Convergence and Computational Efficiency
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Modèles d'endommagement à gradient en grandes déformations
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