解析型弹性地基Timoshenko梁单元

采用双参数弹性地基模型和Timoshenko深梁模型，建立了弹性地基一般梁挠度控制方程，求解得到了挠度方程解析通解，构建了双参数弹性地基深梁的挠度、截面弯曲转角及剪切角的解析位移形函数。建立了梁模型、梁基模型等两种势能泛函，利用最小势能原理，构造了两个双参数弹性地基深梁单元，给出了单元列式。分析表明:梁模型单元在均布荷载作用下误差为0.221%，非均布荷载作用下误差为0；梁基模型单元在均布荷载作用下误差为0，在两端集中力作用下误差为6.597%，在跨中集中力作用下误差为102.716%；同时，该文提出的双参数Timoshenko梁模型单元不存在剪切闭锁的问题。

ANALYTICAL ELEMENT FOR TIMOSHENKO BEAM ON ELASTIC FOUNDATION

Based on a double-parameter elastic foundation model and a Timoshenko deep beam model, the deflection control equation of an elastic foundation beam is deduced, its analytical general solution is obtained, and analytical displacement shape functions for the deflection, section flexural angle and shear angle of a double-parameter elastic foundation deep beam are constructed. The potential energy functions for the beam model and beam-foundation model are established, respectively. The corresponding elements for a double-parameter elastic foundation deep beam are obtained via the minimum potential energy principle, and their element formulas are also received. The calculation results show that the relative error of the element for beam model under a uniformed load is 0.221%, and that under a non-uniformed load is zero. The relative error of the element for the beam-foundation model under the uniformed load is zero, that under a concentrated force at two ends is 6.597%, and that under the concentrated force at mid-span is 102.716%. And there are no shear locking problems with this double-parameter Timoshenko beam element.