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基于薄板的小挠度理论和叠加原理,考虑横向变温情况,将温度作用下的三边简支一边自由矩形薄板看作是面内温差作用下的四边简支矩形薄板和自由边上挠度作用下的三边简支一边自由矩形薄板的叠加,得到了温度作用下三边简支一边自由混凝土矩形薄板的挠度和弯矩解析解。首先通过在自由边界上试设具有待定参数的挠度函数,采用李维解法推导出三边简支一边自由矩形薄板在自由边界挠度作用下的挠度方程;其次利用横向变温作用下四边简支矩形薄板的求解得到待定参数;再采用叠加原理得出横向变温作用下三边简支一边自由矩形薄板的挠度和弯矩解析解;最后利用MATLAB编制程序得到了横向变温作用下三边简支一边自由矩形薄板的计算系数用表,为工程结构中三边简支一边自由混凝土矩形薄板在热环境下的设计计算提供了理论依据。
Based on the theory of small deflection and the principle of superposition, taking the transverse temperature change into consideration, the free rectangular plate with simple support on the three sides under temperature action is regarded as the rectangular thin plate with four edges under the effect of the in-plane temperature difference and the free edge deflection Three-sided simply supported by the free rectangular sheet superimposed, obtained under the action of temperature simply supported on one side of the free-form rectangular plate deflection and bending moment analytical solution. First of all, the deflection equation of the free rectangular plate with one side of free edge under the free boundary deflection is deduced by trying out the deflection function with the parameters to be determined on the free boundary and using the Levi’s solution. Secondly, by using the four-sided simply supported rectangular plate Then get the undetermined parameters by using the superposition principle, and then obtain the analytical solution of the deflection and moment of the free rectangular thin plate with one side of the simple support under lateral temperature change. Finally, the free rectangular The calculation coefficient of the sheet is provided with the table, which provides a theoretical basis for the design and calculation of the free-form rectangular sheet in the thermal environment with simple support of three sides in the engineering structure.