FIRST-ORDER FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL ELASTICITY

In the conventional displacement finite element methods，the stresses are obtained from a differential operation after the nodal displacements are determined． In order to improve the accuracy of the stress，a first-order multivariable form was proposed to make sure that the order of stresses and displacements should be equal，and the weak form was then derived． Using the finite element method，a two-dimensional elastic problem was solved by firstorder method，and the first-order solutions and the solutions of the conventional displacement finite element method were compared． The numerical results showed that the first-order solution effectively improved the accuracy of the stress while the displacement errors and the stress errors had the same convergence order，which verified the effectiveness of the method and provided a new idea of improving the accuracy for the finite element method．