【摘要】 考虑地基水平摩阻的影响,建立Winkler地基上Timoshenko深梁的平衡方程,导出微分方程的初参数解和传递矩阵法,利用初参数解建立有限元列式和单元内均布荷载、集中力、集中力偶等非结点荷载的等效公式。当地基水平劲度系数为0时,地基退化为传统的Winkler地基,当梁的抗剪劲度无穷大时,Timoshenko梁退化为Euler梁,该模型是一种较为通用的模型。利用传递矩阵法和有限元法分析在均布荷载和集中力共同作用下的两端自由Timoshenko梁及在集中力、集中力偶和分布荷载共同作用下的二端自由阶梯梁弯曲问题,讨论Winkler地基、双参数地基、考虑水平摩阻的Winkler地基梁的挠度、转角、剪力、弯矩变化。算例结果表明:传递矩阵法结果与有限元结果完全一致,可相互验证其正确性,有限元精度不依赖于单元划分密度,水平摩阻对弹性地基梁有较大影响。更多还原

【Abstract】 Considering the horizontal friction effect of an elastic foundation,the equilibrium equation for Timoshenko beam on Winkler foundation was derived.The initial parameter solution and transfer matrix method were deduced.Using the initial parameter,a finite element formulation and equivalent nodal forces of distributed load,concentrated load and concentrated moment were presented.If the horizontal friction rigidity of the foundation is zero,the foundation degenerates into a classical Winkler foundation.If shear rigidity of the beam is infinite,Timoshenko beam converts into Euler beam.Using transfer matrix method and finite element method,Timoshenko beams under concentrated load and distributed load with free-free ends,and stepped Timoshenko beam under concentrated load,concentrated moment and distributed load with free-free ends were analyzed.The results from the transfer matrix method were consistent with those from the finite element method,which can validate each other,the precision of finite element does not depend on mesh density,horizontal friction has very important effect on elastic foundation beam.更多还原