应变梯度理论有限元:C0-1分片检验及其变分基础

基于细观有限元弹性应变梯度理论，首次提出应变梯度有限元的C^0-1分片检验条件及其变分基础和一种构造应变梯度单元的方法．与常规的C^0分片检验和C^0分片检验不同，C^0-1分片检验要求检验函数为满足平衡方程的二次函数，并同时通过线性平面应力C^0分片检验和应变梯度常曲率的C^1分片检验．进一步提出一个平面18-DOF三角形应变梯度单元(RCT9 RT9)，算例表明该单元通过C^0-1分片检验，无伪零能模式，并有较高的精度。

Finite element methods in strain gradient theory:C0-1 patch test and its variational basic

Based on finite element formulations for the theory in strain gradient elasticity of microstructures, a convergence criterion for the C ~(0-1) patch test and its variational basic are first introduced. The element displacement function should pass the C ~1 constant curvature patch test and the C ~0 linear stress patch test. The test displacement function for C ~(0-1) patch test should be a complete second-order polynomial that satisfies the equilibrium equation. A new approach to devising strain gradient finite elements that can pass the C ~(0-1) patch test is proposed. 18-DOF plane strain gradient triangular element (RCT9 RT9), which can pass the C ~(0-1) patch test and has no spurious zero energy modes, is proposed. Numerical examples are employed to examine the performances of the proposed element by carrying out the C ~(0-1) patch test. The proposed element possesses higher accuracy compared with other strain gradient elements.