中文摘要：

偶应力理论可以解释微构件力学性能的尺度效应现象,但位移二阶梯度的引入给其数值实施带来一定难度。为降低对试探函数连续性的要求,并避免使用约束变分原理的不足,构造基于控制域的无网格自然邻近伽辽金法。该方法以位移作为唯一场变量,在不引入拉氏乘子或罚函数的情况下放松了对位移场的连续性要求,整体刚度矩阵的计算完全不涉及区域积分,易于实施本质边界条件。

英文摘要：

The couple stress elasticity has the ability to model the size effects of materials in the micron scale.However the introduction of the second-order gradients of displacements in the weak form brings about some difficulties in the numerical implementation.To relax the continuity requirement without using the constrained variational principle,a control domain based meshless natural neighbour Galerkin method is proposed.The displacement is the only field variable and the continuity requirement for the displacement field is relaxed without using either Lagrange multipliers or penalty parameters;domain integrals are avoided in the assembly of the global stiffness matrix;and the imposition of essential boundary conditions is straightforward.