修正的偶应力线弹性理论及广义线弹性体的有限元方法

以含偶应力的弹性理论为基础，考虑小变形情况下变形体的平动变形和旋转变形，提出关于偶应力与曲率张量的线性本构关系，建立一般弹性体的线性模型。为满足有限单元C1连续性要求，考虑转角为独立变量，利用罚方法引入约束条件，构造一般弹性体的约束变分形式。应用8节点48个自由度的实体等参元，建立一般弹性体力学响应分析的有限元方程。对悬臂梁的静力和动力分析表明，一般弹性体模型较之经典弹性力学更适合结构分析；较之Timoshenko梁模型，一般弹性体模型能够计及结构尺度对结构动力特性和动力响应造成的显著影响。

A MODIFIED COUPLE STRESS LINEAR ELASTICITY AND FINITE ELEMENT METHOD FOR GENERALIZED ELASTIC BODIES

Upon on the theory of elasticity with couple-stress, a modified constitutive equation between couple stress and curvature tensor is developed in this paper, taking account of the deformation as a result of translation and rotation in generalized elasticity bodies under infinitesimal deformation. The penalty function method is used to construct the constrained variational form for generalized elasticity, with the rotational angle as independent degree of freedom to relax the C1 continuity in finite element. The finite element equation of motion is given for the generalized elastic body, discretized by elements with 8-nodes and 48 degree of freedom. Static and dynamical analysis of a cantilever beam are presented showing the advantage in structural analysis fields for the generalized elasticity with couple stress effects, comparing to the classic elasticity and structural mechanics. In contrast to the classical elasticity and structural mechanics, the generalized elasticity for deformation body can capture the size dependent effects in material, which have a great influence on the dynamical characteristic of micro-structure.