Bending and vibration analyses of plate and shell using an element decomposition method

Abstract

PurposeThe purpose of this paper is to apply the element decomposition method (EDM) in the study of the bending and vibration properties of plate and shell.Design/methodology/approachIn the present method, each quadrilateral element is first divided into four sub-triangular cells, and the local strains are obtained in those sub-triangles based on linear interpolation. The whole strain filed is formulated through a weighted averaging operation of local strains, implying that only one integration point is adopted to construct the stiffness matrix. To reduce the instability of one-point integration and increase the accuracy of the present method, a stabilization item of the stiffness matrix is formulated by variance of the local strains. A mixed interpolated tensorial components (MITC) method is used in eliminating the shear locking phenomenon.FindingsThe novel EDM based on linear interpolation is effective in bending and vibration analyses of plate and shell, and the present method used in practical problems is reliable for static and free vibration analysis.Originality/valueThis method eliminated the instability of one-point integration and increased the accuracy by a stabilization item and performed stably in engineering analysis including large-scale problems of vehicle components.