含任意椭圆核各向异性板杂交应力有限元

A HYBRID STRESS ELEMENT WITH AN ARBITRARY ELLIPTICAL INCLUSION FOR ANISOTROPIC PLATES

基于含椭圆核有限大各向异性板弹性问题的复变函数级数解,应用杂交变分原理建立了一种与常规有限元相协调的含任意椭圆核各向异性板杂交应力有限元.单元内的应力场和位移场采用满足平衡方程、几何方程与物理方程的复变函数级数解,假设的复变函数级数解精确满足椭圆核边界处的位移协调条件和应力连续条件,单元外边界上的位移场按常规有限元位移场假设,单元内椭圆核的长轴可以与材料主轴不重合.单元刚度矩阵采用Gauss积分求得,并给出了建立刚度矩阵的主要公式和推倒过程.数值计算结果表明该单元具有计算精度高、计算工作量小等优点.

The complex potential method for an anisotropic plate containing an elliptical inclusion and a hybrid variational principle are used to establish a hybrid stress element which assorts with the conformal finite element. The displacement and stress field in the element are the complex variable series solutions satisfying the equilibrium equations, geometric equations and constitutive laws. The assumed complex variable series solutions satisfy exactly the continuum of stress conditions and the consistency of displacement along the elliptical inclusion boundary, while the assumed displacements along the element outer boundaries are the same as the conventional finite element. The axis of the elliptical inclusion can coincide with the material＇s principal axis or not. The element stiffness matrix is numerically obtained by the Gauss quadrature. The main formulae and detailed derivations are given in the paper. The computational results indicate that the high precision can be obtained and less computational cost is spent in the computation process.