厚薄通用板元在厚筏基础中的应用

Timoshenko厚梁理论提供了随梁厚变化的剪应变函数,将其应用于厚板中,得到板剪应变场,此外,假设整个板元的挠度场为不完全四次式,引入广义协调理论,建立了两个变量场的协调方程,从而构建了一个无剪切闭锁的厚薄通用板元。在此基础上,利用最小位能原理,得出考虑转角支撑作用的厚筏基础和Winkler弹性地基的共同作用方程。最后,将其首次应用于实际工程的分析中。

THE APPLICATION OF A GENERALIZED CONFORMING ELEMENT FOR THIN-THICK PLATES IN THE ANALYSIS OF THICK RAFT FOUNDATION

Timoshenko beam theory is applied to get the thick plate’s shearing strain field. In addition, the plate’s deflection field is assumed to be an imperfective polynomial function of four orders. Then, according to generalized conforming theory, the equations combined with the two fields are established. A quadrilateral element for both thin and thick plates is constructed. Based on the minimum potential energy principle with the consideration of the interaction between the plates and Winkler’s foundation, the stiffness equation of element is obtained. In the end, the practicability and accuracy of the fore-mentioned element are proved by an engineering example.