应用功的互等定理求解具有复杂边界条件的矩形板的挠曲面方程
Applications of the Reciprocal Theorem to Solving the Equations of the Deflection Surface of the Rectangular Plates with Various Edge Conditions
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摘要: 本文指出,在一定的条件下,功的互等定理等价于位移叠加原理.在[6]的基础上进一步推广了功的互等定理的应用,因而为求解在复杂受力情况下,具有复杂边界条件的矩形板和直梁的挠曲面方程提供了一个简便、通用的新计算方法.Abstract: This paper points out that on certain condition the reciprocal theorem is equivalent to the superposition principle of displacements. On the basis of [6], applications of the reciprocal theorem are further extended; a convenient, general and new method for solving the equations of deflection surface of the rectangular plates and the straight beams with various edge conditions under various loads is pie-sented.
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[1] 钱伟长,叶开沅,《弹性力学》,科学出版社,(1980,3). [2] 钱伟长,《变分法及有限元》(上册),科学出版社,(1980) [3] 张福范,《弹性薄板》,科学出版社,(1963) [4] 张福范,悬臂矩形板的弯曲,全国弹塑性力学学术交流会论文,(1980,6). [5] Timoshenko,S.and Woinowsky-Krieger.S.,Theorg of Plates and Shell,Second Edition.(1959). [6] 付宝连,求解位移方程的能量原理,应用数学和力学,2,6(1981). -
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