THE LOWER BOUND FINITE ELEMENT METHOD BASED ON STRESS GRADIENTS EXPANSION

Based on Taylor series theory, the stress field of a triangle element can be expanded through center point stress and its stress gradients. Along with the equilibrium equations, which is a linearized relationship of stress gradients, the numbers of variables in a triangle element can be reduced from 9 to 7. Because of pre-satisfied equilibrium, the obtained lower bound mathematical programming model not only decreases the variables, but also reduces the equations, so this programming model has lower models compared with Sloan method. The method enriches the lower bound finite element theory and lays foundation to increase the solving efficiency. The results of examples show this method can get the same results as Sloan method gets.