Boundary Conditions and Mode Jumping in the von Kármán Equations

DOI10.1137/0515034zbMath0542.73057OpenAlexW2037740421MaRDI QIDQ3330646

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Publication date: 1984

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0515034

zbMATH Keywords

Lyapunov-Schmidt reductionvon Kármán equationsplate deflectiondouble eigenvaluemode jumpingtwo types of boundary conditionspostbuckling responseDirichlet typeNeumann typelong rectangular plate

Mathematics Subject Classification ID

Plates (74K20) Bifurcation and buckling (74G60) Bifurcations in context of PDEs (35B32)

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A unilateral contact model with buckling in von Kármán plates ⋮ Multimode bifurcations of elastic equilibria ⋮ The projective-iterative method and neural network estimation for buckling of elastic plates in nonlinear theory ⋮ On the bifurcation of solutions to Marguerre-von Kármán equations ⋮ Elastic rods with incompatible strain: macroscopic versus microscopic buckling ⋮ Sharp estimates for the global attractor of scalar reaction-diffusion equations with a Wentzell boundary condition ⋮ Bifurcations of the von Kármán equations with Robin boundary conditions ⋮ The spectral method and numerical continuation algorithm for the von Kármán problem with postbuckling behaviour of solutions ⋮ Finite element analysis of the buckling and mode jumping of a rectangular plate ⋮ A time spectral method for solving the nonlinear dynamic equations of a rectangular elastic plate ⋮ Forced symmetry-breaking via boundary conditions ⋮ Buckling and postcritical behaviour of the elastic infinite plate strip resting on linear elastic foundation ⋮ Tracing the buckling of a rectangular plate with the block GMRES method ⋮ A cubic Hermite finite element-continuation method for numerical solutions of the von Kármán equations

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