基于双模量理论的均布载荷下简支梁的解析解及数值分析

ANALYTICAL SOLUTION AND NUMERICAL ANALYSIS FOR SIMPLY SUPPORTED BEAMS UNDER UNIFORMALY DISTRIBUTED LOADS BASED ON BIMODULAR THEORY

放弃平截面假设,利用拉压分区的简化力学模型,导出均布荷载下双模量简支梁的解析解。基于双模量有限元数值迭代技术,引入具有收敛特性的剪切模量,建立同一问题的数值迭代模式,计算了不同拉压模量比值情形下的从浅梁到深梁的弯曲问题,数值计算结果表明,材料的拉压不同弹性模量特性对梁的弯曲应力和挠度有较大的影响。通过解析解计算结果和数值计算结果的对比分析,确定了所给出的解析解的合理适用范围。

In this paper, by using a simplified mechanical model on subarea in tension and compression, the analytical solution of bimodular simply supported beams under uniformly distributed loads was derived without the assumption of plane section. Based on the numerical iteration technique from bimodular finite element method, the shear modulus used for accelerating convergence was introduced and the numerical iterative program for the same problem was rebuilt. Using this program, bimodular beams in the cases of different ratios of elastic moduli in tension and compression, including from shallow beams to deep ones, are computed. The numerical result shows that different ratios of elastie moduli has great influences on the bending stresses and the vertical deflection of bimodular beams. By contrasting the numerical results with the analytical solutions, the applicable range of the analytical solutions presented in this paper was determined.