SOLVING IMBEDDING PROBLEMS IN THREE-DIMENSIONAL CONTACT ELEMENT WITH THE 'PENALTY FUNCTION' METHOD

摘要

In this paper, the classic 'penalty function' method based on constrained variational principle is applied to solve the imbedding problems of upper and lower surfaces of three-dimensional contact (or joint) elements. The critical imbedding or impenetrability constraint condition is defined as the equivalency of the close displacement of the upper and lower surfaces to the element thickness. If this critical impenetrability constraint condition is broken, a modification should be made to the element stiffness matrix and nodal force vector. By calculating the extremum of contact elements' function under the critical impenetrability constraint condition, the incremental three-dimensional contact finite elements formulations are obtained, and the modified contact stiffness matrix and contact load vector are derived and superimposed to the general stiffness matrix and load vector. An iterative algorism is processed to guarantee that the imbedding displacement is modified to a very tiny numerical value and the imbedding problems are corrected. At the end, an incremental finite element program chart is presented to show how to use this method to solve the imbedding problems of three-dimensional contact elements.