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在各种边界条件下任意四边形钢筋砼板的变形分析计算,在土建工程的钢筋砼结构中十分重要。因为在这方面既存在巨大浪费而又不被设计人员所重视。从亚微观结构形式看,钢筋砼板的变形比较适合于用能量来描述。首先建立钢筋砼板的能量泛函;其次,由于板的形状为任意四边形,故还需建立直角坐标与参数坐标间的计算转换关系;再采用康托洛维奇-加权残数法,建立钢筋砼板的变形分析微分方程及其求解;最后用实例验证表明,这种方法具有原理清晰、精度高等特点,是计算弹性地基上任意四边形板的有效方法。
Deformation analysis and calculation of arbitrary quadrangular reinforced concrete slab under various boundary conditions is very important in the reinforced concrete structure of civil engineering. Because there is a huge waste in this area without the designer’s attention. From the perspective of submicroscopic structure, the deformation of reinforced concrete slabs is more suitable for describing with energy. Firstly, the energy functional of the reinforced concrete slab is established. Secondly, since the shape of the slab is arbitrary quadrilateral, the relation between the rectangular coordinate and the parameter coordinate needs to be established. Then, using the Cantorovich-weighted residual method, Deformation analysis of concrete slab differential equation and its solution; Finally, with examples verified that this method has the principle of clear, high precision, is an effective method for calculating arbitrary quadrilateral plate on the elastic foundation.