拉压弹性模量不同材料板的热弯曲及屈曲

Thermal bending and buckling calculations of bimodulous plate

为了分析拉压弹性模量不同材料板在热状态下的力学行为,采用弹性理论研究了拉压弹性模量不同材料板的热弯曲及屈曲问题。建立了拉压弹性模量不同材料板在热状态下的弯曲微分方程,推导出了相关板热弯曲的解析解;选取梁函数作为试函数,采用Galerkin原理推导出了热屈曲时的临界载荷,该方法计算结果与有关文献计算结果的误差很小;并讨论分析了长宽比、温度对拉压弹性模量不同材料板热弯曲及屈曲的影响。研究结果表明:拉压弹性模量不同材料四边简支矩形板的中点弯曲挠度随着长宽比的增大逐渐变小,而随着温度比增大拉压弹性模量不同材料四边简支矩形板中点弯曲挠度也逐渐增大;当拉压弹性模量相差较大时,采用单模量弹性理论研究拉压弹性模量不同材料板热弯曲及屈曲是不合适的。

In order to analyze the mechanical behavior of bimodulous plate in thermal state, the thermal bending and buckling calculations of bimodulous plate were studied by using elastic theo- ry. Thermal bending differential equations for the bimodulous plate were established and the ana- lytical solution to thermal bending calculation of relevant plate was derived. Galerkin principle was used to deduce the critical load of thermal buckling by taking beam functions as trial func- tions, and the calculation errors were very small. The effects of length-width ratio and tempera- ture on thermal bending and buckling of the bimodulous plate were discussed and analyzed. The results show that as the ratio of length to width increases, the midpoint deflection of bimodulous rectangular plate with simple support decreases gradually as the temperature ratio increases, the midpoint deflection of bimodulous rectangular plate with simple support also increases. Analysis on examples indicates that it＇s in appropriate to use elastic theory with same elastic modulus to study the thermal bending and buckling calculations of bimodulous plate with different tensile e- lastic modulus and compressive elastic modulus. 4 tabs, 3 figs, 13 refs.