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本文采用三次修正B样条的线性组合作插值函数,根据弹性薄板的广义变分原理对带有复杂边界条件的矩形薄板建立了总体刚度矩阵,给出了系数矩阵的显式表达式。另外,本文还利用叠加原理对内、外边界均为矩形的开孔薄板建立了总体刚度矩阵,给出了系数矩阵的显式表达式。文中提出的计算方法具有精度高、计算量少、易于在小型计算机上实现等特点,应用甚为简便。最后,文中给出的若干算例说明本文提出的方法的计算精度能满足工程设计要求。
In this paper, the linear group cooperative interpolation function of cubic modified B-spline is adopted. According to the generalized variational principle of elastic thin plate, the overall stiffness matrix of rectangular thin plate with complex boundary conditions is established. The explicit expression of coefficient matrix is given. In addition, we use the principle of superposition to establish the overall stiffness matrix for open-pored thin plates whose inner and outer boundaries are rectangular, and give the explicit expressions of coefficient matrix. The calculation method proposed in this paper has the characteristics of high precision, low computational complexity, and easy implementation on small computers. The application is very simple. Finally, some examples given in the paper show that the calculation accuracy of the proposed method can meet the engineering design requirements.