【摘要】 基于梯度板结构的渐近均匀化方法，简化梯度板微单胞的单胞方程及等效刚度列式，并推导其有限元求解列式，实现梯度加筋板微结构等效刚度的高效数值求解。相比仅能处理矩形单胞的经典数值均匀化方法，该方法可以处理一般平行四边形微结构，具有更好的普适性。数值算例通过比对梯度加筋板及其对应的等效均质板挠度，最大挠度数值相对误差均在5%以内，验证了所提数值方法的正确性及可行性。更多还原

【Abstract】 Based on the asymptotic homogenization method of gradient plates, the unit cell problems and the effective stiffness of gradient plates are simplified, and the finite element solution is derived to achieve the efficient numerical solution of effective stiffness. Compared with the classical numerical homogenization method which can only deal with rectangular cells, this method can deal with general parallelogram microstructure and has good universality. The numerical examples verifies the correctness and feasibility of the numerical method proposed in this paper by comparing the deflection of the gradient stiffened plate and its corresponding equivalent homogeneous plate, and the relative error of the maximum deflection value is within 5%.更多还原