均布静水压力下椭圆环的内力和位移分析

An Analysis of the Internal Force and Displacement in Elliptical Rings under Uniform Hydrostatic Pressure

分析均布静水压力下椭圆环的内力和位移,对椭圆环结构的机电产品和土建结构等的设计制造、安装调试和维护保养等具有一定的工程意义。用能量法导出均布静水压力下椭圆环的内力和位移的计算公式。以水平轴与铅垂轴长度之比k为2的椭圆环为例,绘制了无量纲化的内力图和位移图,分析了内力和位移的零点、极值点和极值:弯矩方面,极值点在两条轴上,最大弯矩在长轴上,零点不在两条轴上;轴力方面,极值点在两条轴上,最大轴力在长轴上,轴力始终为压向;剪力方面,极值点不在两条轴上,零点在两条轴上。沿短轴的位移方面,极值点在短轴上,零点在长轴上;沿长轴的位移方面,极值点在长轴上,零点在短轴上;角位移方面,极值点不在两条轴上,零点在两条轴上。

The analysis of the internal forces and displacements of elliptic rings under uniform hydrostatic pressure is of significance in engineering for the design,manufacture,installation and maintenance of relevant electromechanical products and civil structures.The energy method was used to derive the formula for the internal forces and displacements of elliptical rings.With the elliptic ring,the length ratio k between its horizontal and vertical axis being 2,as an example,the dimensionless diagrams of internal forces and displacements were drawn,and the relevant zero-point,extreme-point and extreme-value were analyzed.The results are as follows:for bending moment,the extreme-points are on both axes with the maximum bending moment on the long axis while the zero-points are on neither axis;for axial force,the extreme-points are on both axis with the largest force on the long axis and the axial force always in pressure direction;for shear force,the extreme-points are on neither axis while the zero-points are on both axes.In addition,in terms of displacement along the short axis,the extreme-points and the zero-points are on the short and the long axis respectively,while the reversed results are obtained in terms of displacement along the long axis;the results regarding angular displacement are identical to those of shear force.