复杂载荷下变刚度静不定梁程序化求解

COMPUTERIZED SOLUTION OF STATICALLY INDETERMINATE BEAMS WITH VARYING FLEXURAL RIGIDITY UNDER COMPLEX LOAD

对于有复杂载荷的变刚度静不定梁,常用的方法无法求解。建立一种复杂载荷下变刚度静不定梁求解的通用力学模型,从该模型推导出任一截面的转角和挠度变形方程,由变形方程得出静不定梁程序化求解的通用矩阵。用Matlab语言开发出相应的静不定梁求解程序,实现了对复杂载荷变刚度静不定梁的计算机求解。在静不定梁模型建立和求解推导过程中,不需进行载荷和梁结构的简化,对静不定梁两端的支承形式也没有限制,是一种适于应用计算机编程进行求解的通用计算方法,实际应用效果很好。

For statically indeterminate beams with varying flexural rigidity, it is difficult to develop rigorous solution using routine approaches. A general model for statically indeterminate beams with varying flexural rigidity under complex load is established in this paper. The equations of the rotational angle and the deflection are given and the general matrix for computerized solution is derived. A program is developed using MATLAB. It is shown that the present approach is general since no simplification of load and structure or restriction on the end conditions of beam is introduced in the solution process.