加权残值法计算薄板的临界压力

弹性薄板屈曲的临界压力计算,在弹性力学中一般都是采用双三角级数解法,计算过程比较复杂,工程中应用不方便.同时薄板的临界压力在很多情况下得不到准确的解析结果,所以求解薄板临界压力的近似解在工程设计中很有必要.加权残值法是求解微分方程近似解的一种有效的数学方法,广泛应用于各种工程技术领域.为了简化计算过程,得到有用的近似解,利用加权残值法与康脱洛维奇变分原理,以第二类切比雪夫多项式和三角函数作为试函数,求解矩形薄板在不同支承条件下屈曲时的临界压力.通过实例计算表明这种方法计算简单,具有一定的精确度,在工程实际中应用方便.

Calculating Critical Loads of Thin Plates With Method of Weighted Residuals

In elastic mechanics, it is common practice to calculate critical loads in buckle of thin plates by means of double triangle series. The calculation process is more complex, this method has not facility in engineering application. In many cases critical loads of thin plates can not obtain precise analytic solutions. It is very important to solve approximate resolutions of critical loads of plates in engineering. The method of weighted residuals is an available measure to solve proximal resolutions of differential equations and has extensive application in egineering. In order to simplify calculation process and obtain profitble result, by means of method of weighted residuals and Cantorovich variational principle, taking the second Tchebychev's polynomials as trial functions, it was calculated, critical loads of rectangle thin plates in different supporting conditions. Calculation results indicate that this calculation method is simple and has some precision, it is applied conveniently in engineering.