A group-theoretic approach to computational bifurcation problems with symmetry

DOI10.1016/0045-7825(88)90049-7zbMath0668.73041OpenAlexW1988010545MaRDI QIDQ1118452

Timothy J. Healey

Publication date: 1988

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(88)90049-7

zbMATH Keywords

bifurcation pointshexagonal symmetrygroup invariancelimit pointsequivariance propertiesglobal solution brancheslattice- dome structureparameter-dependent equations

Mathematics Subject Classification ID

Bifurcation and buckling (74G60) Generalities, axiomatics, foundations of continuum mechanics of solids (74A99) Thin bodies, structures (74Kxx) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (29)

Exploitation of symmetry in graphs with applications to finite and boundary elements analysis ⋮ On group‐theoretic computation of natural frequencies for spring–mass dynamic systems with rectilinear motion ⋮ Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the \(D_4\) symmetry group; interpolation within a squircle. I ⋮ Postbuckling behavior and imperfection sensitivity of elastic structures by the Lyapunov-Schmidt-Koiter approach ⋮ A group theoretic approach to the global bifurcation analysis of an axially compressed cylindrical shell ⋮ Reversible stress-induced martensitic phase transformations in a bi-atomic crystal ⋮ Symmetry and equivariance in nonlinear elastostatics. I ⋮ Computational methods for bifurcation problems with symmetries - with special attention to steady state and Hopf bifurcation points ⋮ Symmetry and asymmetry of solutions in discrete variable structural optimization ⋮ On the number of matrices to generate a matrix \(\ast\)-algebra over the real field ⋮ Gröbner bases plugged into graphical skills to solve a set of multiple bifurcation equations in structural compound stability problems ⋮ A group-theoretic approach to the bifurcation analysis of spatial Cosserat-rod frameworks with symmetry ⋮ Canonical forms for symmetric and regular structures ⋮ Some computational aspects of a group theoretic finite element approach to the buckling and postbuckling analyses of plates and shells of revolution ⋮ Stable spatially localized configurations in a simple structure -- a global symmetry-breaking approach ⋮ Multiple bifurcation paths visualized by a computational asymptotic stability theory ⋮ The role of symmetry in the post-buckling behaviour of structures ⋮ On the decomposition of generalized eigenproblems for the free vibration analysis of cyclically symmetric finite element models ⋮ Bifurcation analysis of symmetric structures using block-diagonalization ⋮ Modified stiffness iteration to pinpoint multiple bifurcation points. ⋮ Multi-solution theory of signal processing based on finite element method ⋮ Efficient finite element solution of regular and near-regular systems using graph products ⋮ On domain symmetry and its use in homogenization ⋮ Direct computation of two-phase icosahedral equilibria of lipid bilayer vesicles ⋮ Group-theoretic exploitations of symmetry in computational solid and structural mechanics ⋮ Improvement of the scaled corrector method for bifurcation analysis using symmetry-exploiting block-diagonalization ⋮ A criterion for symmetric tricritical points in condensed ordered phases ⋮ Appropriate number of unit cells in a representative volume element for micro-structural bifurcation encountered in a multi-scale modeling ⋮ Group-theoretic method for efficient buckling analysis of prestressed space structures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Group theoretic methods in bifurcation theory. With an appendix by P. Olver
• Some computational aspects of the stability analysis of nonlinear structures
• Pattern selection with \(\mathrm{O}(3)\) symmetry
• Singularities and groups in bifurcation theory. Volume I
• The implicit function theorem and the global methods of cohomology
• Discrete approximations related to nonlinear theories of solids
• The Computation of Symmetry-Breaking Bifurcation Points
• Computation of symmetry modes and exact reduction in nonlinear structural analysis
• Bifurcation and symmetry breaking in applied mathematics
• The Calculation of Turning Points of Nonlinear Equations
• Numerical Methods for a Class of Finite Dimensional Bifurcation Problems
• Material Symmetry and Chirality in Nonlinearly Elastic Rods
• Convergence Cones Near Bifurcation
• The Application of Newton’s Method to the Problem of Elastic Stability
• Approximate Solutions of Transport Problems. II. Convergence and Applications of the Discrete Ordinate Method

This page was built for publication: A group-theoretic approach to computational bifurcation problems with symmetry