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对功能梯度板的固有频率优化问题进行研究.从无网格方法自然单元法出发,建立了功能梯度板的一阶剪切变形理论的自由振动分析格式.自然单元法是一种基于自然邻近插值的无网格数值方法.自然邻近插值不涉及矩阵求逆运算,也不需要任何人为的参数.较之于传统复合材料,功能梯度板材料属性沿厚度方向呈梯度连续变化,因此材料加工时产生的残余应力小很多,此外,功能梯度板具有可设计的优点.以第一阶固有频率为优化目标建立优化模型,通过单纯形法搜索较优的功能梯度板的成分分布.最后通过矩形功能梯度板在不同边界条件下的基频优化的实例,验证了整个算法的可行性和有效性.
Based on the natural element method of meshless method, the free vibration analysis format of the first-order shear deformation theory of functional gradient plate is established.Natural element method is a method based on natural neighbor interpolation The meshless interpolation method does not involve matrix inversion and does not require any artificial parameters.Compared with the traditional composite materials, the function of the gradient plate material changes continuously along the thickness gradient, so the material processing time In addition, the functionally graded plate has the advantages of designability.Optimize the model with the first-order natural frequency as the optimization objective and search the compositional distribution of the better functionally graded plate by simplex method.Finally, through the rectangular function gradient The example of the fundamental frequency optimization of the board under different boundary conditions verifies the feasibility and effectiveness of the whole algorithm.