Geometric non‐linear analysis of folded plate structures by the spline strip kernel particle method

Abstract

SUMMARYThis paper investigates the geometric non-linear behaviour of stiffened and un-stiffened folded plate structures using the spline strip kernel particle method (SSKPM). The first-order shear deformable plate theory and large deflection theory of von Karman are employed. The folded plate structures are considered as assemblies of individual stiffened and un-stiffened flat plates that lie on different planes. We regard these stiffened and un-stiffened plate structures as superelements, and superpose their stiffness matrices to derive the final global stiffness matrices. Several numerical example problems are examined, and comparison studies are carried out with other available results. The effect of the size of the support, the order of the polynomial basis functions, and the spacing of the spline nodes on the convergence of the proposed method is examined.

Static and frequency optimization of folded laminated composite plates using an adjusted Differential Evolution algorithm and a smoothed triangular plate element

“…(12), at the positions corresponding to drilling degrees of freedom, all components of membrane strain gradient matrix are non-zero. This hence helps overcome the singularity phenomenon mentioned in Eq.…”

“…(11) by the matrix B Allman m in Eq. (12), we obtain the equation for computing the element stiffness matrix in the global coordinate system of the coupled method (including the plate element CS-DSG3 and the Allman's plane stress element) as…”

“…This is because folded plate structures possess many advantages such as lightweight, easy manufacture, suitable cost, and high load carrying capacity compared to flat plates. Due to such superior characteristics and wide range of application, the analyses of folded plate structures have attracted a certain attention from researchers around the world [1][2][3][4][5][6][7][8][9][10][11][12]. Goldberg and Leve [1] are regarded as the first persons to give the exact static solution of folded plates.…”

An element‐free analysis of mechanical and thermal buckling of functionally graded conical shell panels

“…Mesh‐free methods, in which interpolations are based on a set of scattered nodes rather than meshes, have been applied to a variety of engineering problems since their invention. Notable applications include the deformation of thin shells 28–30, folded plate structures 31, 32, static analysis of functionally graded 33 and laminated composite plates 34, vibration of rotating shells 35, modeling of human proximal femur 36, transient thermoelastic deformation of thick functionally graded plates 37, and analysis of elasto‐plasticity problems 38.…”

A meshless method for the nonlinear von Kármán plate with multiple folds of complex shape

“…Notable examples in the meshfree literature include [21,22], where the fold geometry is introduced a priori, by joining different plates through boundary conditions. A meshfree method discretises each plate, and the folded plate is an assembly of individual plates.…”