Finite-element Geometric Stiffness Matrix Lumping by Numerical Integration for Stability Analysis

Using numerical integration in the formulation of the finite-element geometric stiffness matrix and placing movable nodes at integration points causes the geometric stiffness matrix to become lumped or diagonal. The consistent geometric stiffness matrix which is a non-diagonal matrix, is normally used in the finite-element eigenvalue buckling problem. Altering the method to deliver a diagonal (lumped) geometric stiffness matrix simplifies the process of solving the eigenvalue problem and results in computational savings. The advantage of the diagonal geometric stiffness matrix, also called the lumped force stiffness matrix, is that it usually provides lower buckling loads than the magnitude of the true buckling load. As an example of the method, the lumped force stiffness matrix formulation using the numerical integration is presented for the beam, shell, and rectangular plate elements.