二次有限元格式高阶数值模拟矢量型弹性方程stress边值问题

Higher-order numerical simulation of quadratic finite element scheme for vector-type elastic equation with stress boundary

针对具有stress边值的矢量型弹性力学问题,利用二次有限元计算格式实现高阶数值模拟.基于有限元方法的三角形剖分,在线性基函数基础上构造更有效的二次基函数,通过节点位移及其偏导数刻画应力张量和应变张量,形成对应分量的代数方程组,并限定边界的法向量和切向量模拟stress边值细节.理论分析和数值实验表明:有限元解能够充分逼近矢量型方程的真解,且二次有限元格式在误差范数度量下精度更好,收敛更快.

A vector-type elastic problem with a stress boundary is studied,and a higher-order numerical simulation is achieved via proposing a quadratic finite element scheme.Based on the triangular subdivision of finite element method,a more efficient quadratic basis function is constructed based on the linear basis function.The stress and strain tensors are described by the node displacement and its partial derivatives,and the algebraic equations for components of vector are formed respectively.Through refining its normal vector and tangent vector of the stress boundary,the boundary details are confirmed.Theoretical analysis and numerical experiments show that the finite element solution can fully approximate the true solution of vector-type,and the quadratic finite element scheme has better accuracy and faster convergence under the error norm measurement.