A numerical method for linear two-point boundary-value problems using compound matrices

A practical method for the evaluation of eigenfunctions from compound matrix variables in finite elastic bifurcation problems

“…If it is only the displacement f that is required we do not need anything further and we simply have to solve the third order system. If, however other displacements are required then, in a similar way, by choosing (23) 2,4,6 to solve for C 1 …”

“…It has been found that the trivial boundary conditions naturally associated with similar problems in fluid mechanics leads to a much simpler calculation for the eigenfunctions, see [3][4][5]. With this in mind, we reexamine the solid mechanics bifurcation problem but we now focus attention on the boundary conditions for the original eigenvalue problem.…”

Wkb And Numerical Compound Matrix Methods For Solving The Problem Of Everted Neo-hookean Spherical Shell

“…We know for capital value (1) and (3) with capital exponent and small (2) and (4) . In order to obtain nontrivial solution for equation (27) the following condition must be satisfied:…”

Long wavelength bifurcations and multiple neutral axes of elastic layered structures subject to finite bending

“…The compound matrix method was initially proposed in [Backus and Gilbert 1967] and applied to problems of fluid mechanics [Backus and Gilbert 1967;Ng and Reid 1979a;1979b;1985, Anturkar et al 1992Yiantsios and Higgins 1988] and solid mechanics [Lindsay 1992;Lindsay and Rooney 1992]. Haughton and Orr [1995] used the method in incremental elasticity, while Haughton [1999], Dryburgh and Ogden [1999] and Destrade et al [2009; employed it to investigate instabilities of a homogeneous block subjected to finite flexure.…”