轴对称线布荷载作用下变厚度旋转扁薄壳的非线性稳定

针对轴对称线布荷载作用下变厚度板壳的大挠度的复杂计算,以三次B样条函数为试函数,用配点法计算变厚度旋转扁薄壳的非线性稳定.给出了在线布荷载作用下,线性或多项式变厚度的圆锥壳、球壳或四次多项式壳的上、下临界荷载.多数的解答同其他方法的结果做了比较(包括有限单元法).等厚度球壳的矢高为其厚度的6 052倍时,对上临界荷载的计算仍取得了收敛的数值结果.样条配点法具有精度高和计算程序通用的优点.

Nonlinear Stability of Revolutionary Shells with Arbitrarily Variable Thickness Subjected to Axisymmetric Distributed Line Load

To simplify the complexity of calculating the large deflection of a plate or shell with variable thickness under the action of distributed line load,the solutions of nonlinear stability of revolutionary shells with variable thickness are obtained using the point collocation method with the cubic B-spline function as a trial function.Under the action of distributed line load,upper and lower critical loads of conical shells,spherical shells or quartic polynomial shells with linearly or polynomially variable thickness are obtained.Most solutions are compared with those obtained by other methods(including the finite elements method).As the rise of a spherical shell with uniform thickness reaches 6 052 times its thickness,upper critical load of the shell subjected to distributed line load remains convergent.The program written by the spline collection method are accurate and universal.