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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。
Abandon the assumption of the cross-section, using the simplified mechanical model of tension-compression zone, the analytic solution of the double-modulus simply supported beam under uniform load is deduced. Based on the bimodal finite element numerical iteration technique, the shear modulus with convergence property was introduced to establish the numerical iteration mode of the same problem. The bending problem from shallow beam to deep beam under different ratios of tensile and compressive modulus was calculated. The calculation results show that the different elastic modulus characteristics of the material under tension and compression have a greater impact on the bending stress and deflection of the beam. By analyzing and comparing the result of calculation and the result of numerical calculation, the reasonable range of application of the analytical solution is determined.