不同拉压模量弹性地基梁的解析解

采用拉压不同模量理论,推导了不同模量弹性地基梁的解析解.研究得到的解析解拓展了经典力学理论,并且当拉压模量相同时,该解可以退化到经典理论解.将结果与经典力学同模量理论比较表明:研究得到的解析解能很好地考虑了拉压不同模量效应.为此,合理设计材料的拉压模量比值,可以显著的改变地基梁的弹性特征值、内力及挠度值.该理论遵循材料实际的力学行为,在实际工程设计中大大提高了材料的利用率,达到节约能源的目的,具有重要的工程意义.

Closed-form Analytical Solution for Beam on Elastic Foundation with Different Tension and Compression Modulus

On the basis of the theory of different modulus, the closed-form analytical solution for beams on elastic foundations with different modulus has been derived. A comparison is made between the results of the analytical solution and those calculated from the classic mechanic theories, in which the tension modulus are equal to the compression modulus. It is shown from the numerical results that the ratio of compressive modulus to tensile modulus will greatly affect the elastic characteristic values,internal forces and flexibilities. The present theory satisfies the mechanical behavior of materials. The amount of materials can be economized through rational design by using the elastic theory of different modulus.