Some computational aspects of the stability analysis of nonlinear structures

DOI10.1016/0045-7825(84)90078-1zbMath0535.73062OpenAlexW2012868077MaRDI QIDQ791352

Publication date: 1984

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(84)90078-1

zbMATH Keywords

perturbation method continuation method review instability phenomena

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Stability of dynamical problems in solid mechanics (74H55) Numerical and other methods in solid mechanics (74S99)

Related Items (50)

On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms ⋮ A quadratically convergent procedure for the calculation of stability points in finite element analysis ⋮ A new iterative numerical continuation technique for approximating the solutions of scalar nonlinear equations ⋮ Electromechanical macroscopic instabilities in soft dielectric elastomer composites with periodic microstructures ⋮ A group theoretic approach to the global bifurcation analysis of an axially compressed cylindrical shell ⋮ On the solution of mode jumping phenomena in thin-walled shell structures ⋮ The post-critical analysis of axisymmetric hyper-elastic membranes by the finite element method ⋮ A critical displacement approach for predicting structural instability ⋮ A group-theoretic approach to computational bifurcation problems with symmetry ⋮ A seven-parameter spectral/\(hp\) finite element formulation for isotropic, laminated composite and functionally graded shell structures ⋮ ANM for stationary Navier-Stokes equations and with Petrov-Galerkin formulation ⋮ Direct evaluation of the `worst' imperfection shape in shell buckling ⋮ A Koiter-Newton approach for nonlinear structural analysis ⋮ Combining arc‐length control and line searches in path following ⋮ A model for hyperelastic rubber-like materials based on micro-mechanical elements ⋮ Nonlinear steady state vibrations of beams made of the fractional Zener material using an exponential version of the harmonic balance method ⋮ An algebraic geometric method to calculate branches near a bifurcation point ⋮ A multilevel computational strategy for handling microscopic and macroscopic instabilities ⋮ A predictor algorithm for fast geometrically-nonlinear dynamic analysis. ⋮ Large deflection and post-buckling analysis of shell structures ⋮ A scheme for tracing the equilibrium path in perturbation methods ⋮ On the in-plane failure and post-failure behaviour of pristine and perforated single-layer graphene sheets ⋮ Some computational aspects of a group theoretic finite element approach to the buckling and postbuckling analyses of plates and shells of revolution ⋮ Discussion about parameterization in the asymptotic numerical method: application to nonlinear elastic shells ⋮ Computing finite rotations of shells by an asymptotic-numerical method ⋮ Evaluation of simple bifurcation points and post-critical path in large finite rotation problems ⋮ A quadratically convergent algorithm for the computation of stability points: the application of the determinant of the tangent stiffness matrix. ⋮ Nonlinear analysis based on homogeneous incremental systems ⋮ Combination of the critical displacement method with a damage model for structural instability analysis ⋮ Path following and critical points for contact problems ⋮ Optimization of composite, stiffened, imperfect panels under combined loads for service in the postbuckling regime ⋮ On the behaviour of the ANM continuation in the presence of bifurcations ⋮ A predictor-corrector method for structural nonlinear analysis. ⋮ ON THE SIGN OF THE DETERMINANT OF THE STRUCTURAL STIFFNESS MATRIX FOR DETERMINATION OF LOADING INCREMENT IN ARC-LENGTH ALGORITHMS ⋮ EVALUATION OF THE FOLD LINE BY ASYMPTOTIC EXTRAPOLATION FOR STRUCTURAL ANALYSIS ⋮ A solver combining reduced basis and convergence acceleration with applications to non‐linear elasticity ⋮ Geometrical nonlinear analysis based on optimization technique ⋮ Determination of travel directions in path-following methods ⋮ Stabilized forms of orthogonal residual and constant incremental work control path following methods ⋮ Nonlinear stability-analysis of shell and contact-problems including branch-switching ⋮ A robust Riks-like path following method for strain-actuated snap-through phenomena in soft solids ⋮ Mixed formulation and locking in path-following nonlinear analysis ⋮ Improvement of the scaled corrector method for bifurcation analysis using symmetry-exploiting block-diagonalization ⋮ An effective parametrization for asymptotic extrapolations ⋮ An iterative process based on homotopy and perturbation techniques ⋮ Post-critical analysis of structures with a nonlinear pre-buckling state in the presence of imperfections. ⋮ Computational homogenization analysis in finite elasticity: material and structural instabilities on the micro- and macro-scales of periodic composites and their interaction. ⋮ Nonlinear analysis of elastic thin-walled shell structures. ⋮ Consistent linearization for path following methods in nonlinear FE analysis ⋮ An iterative method for shakedown analysis.

Cites Work

This page was built for publication: Some computational aspects of the stability analysis of nonlinear structures