The quintic finite element and finite strip with generalized degrees of freedom in structural analysis

Abstract

This paper presents the method of quintic finite element and quintic finite strip with generalized degrees of freedom (DOF) based on the philosophy that the local displacement fields of an element or strip should be compatible with the global displacement field. At first, the global displacement field of a structure is developed using the quintic B-spline functions. Then, the local displacement field of element/strip is constructed employing the multi-term interpolation functions of degree 5. At last, the displacement field of finite element/strip with generalized DOF is generated when the local and global displacement fields are equally matched in their deformation. This kind of high order finite element/strip can not only effectively widen the scope of application of the conventional quintic element/strip and the spline function method, but also greatly reduce the amount of DOF with the same degrees of accuracy as compared to the conventional finite element method. Several numerical examples demonstrate the accuracy, simplicity and versatility of the present methods for analysis of thin-walled structures.