局部固支功能梯度板的横向弯曲研究

研究了局部固支功能梯度方板在横向均布载荷作用下的静力学问题。假设功能梯度材料由陶瓷和钢组成,材料弹性模量设计为沿着板的厚度方向按照幂指数形式连续变化,功能梯度方板的四个边均为局部固支,应用Kirchhoff薄板理论和虚功原理推导了板的静力学有限元方程。另分别考虑了各边50%固支和25%固支两种情况,在板材料为纯陶瓷和纯钢时,将所得结果与ANSYS软件结果对比,验证了所建模型的准确性。最后,重点分析了梯度指数对板面和边界最大挠度的影响。结果表明梯度指数和固支范围是决定最大挠度的关键参数,其中固支范围对边界上最大挠度的影响更大。

TRANSVERSE BENDING OF LOCALLY CLAMPED FUNCTIONAL GRADED PLATES

The statics of a functional graded square plate with local clamped support under uniform lateral load is studied. Assuming that the functional graded material is composed of ceramic and steel, the Young''s modulus of the material is designed to change continuously along the thickness of the plate in a power exponential form. Four edges of the plate are locally fixed. The static finite element equations of the functional graded square plates are derived by Kirchhoff plate theory and virtual work principle. When the plate material is pure ceramic and steel, the obtained results are compared with those of ANSYS software to verify the accuracy of the present model. Then, the influence of gradient index change on the maximum deflection of plate and boundary is analyzed. The results show that the gradient index and the clamped range are the key parameters to determine the maximum deflection, and the clamped range has more influence on the maximum deflection of boundary.