Development of Mixed Finite Element Analysis Method for Laminated Rubber Bearing

由橡胶板和钢板组成的叠层橡胶支座已广泛应用于基础结构的减震中。该支座的作用是支撑结构的全部重量，并保护结构免受地震引起的剪切振动。由于超弹性的不可压缩性，基于位移的有限元解会导致压力解的较大误差。为了克服这一缺点，提出了一种混合方法，其中压力场和位移场作为独立变量。有限元解依赖于形函数和数值积分技术;然而，叠层橡胶支座的合适数值条件尚未得到充分讨论。本文给出了超弹性率形式的混合有限元公式，并给出了二维和三维叠层橡胶支座系统剪切变形的数值算例，以阐明该分析方法的优点和力学响应的基本特征。

The laminated rubber bearing consisting fo rubber sheets and steel plates has been widely used in base structures to absorb earthquake vibration. The function of this bearing is to support all the weight of the structure and protect the structure from shear vibration by earthquake. Due to the nearly incompressible property of hyperelasticity, the displacement-based finite-element solutions cause large errors in pressure solutions. In order to overcome this shortcoming, a mixed method has been proposed, where pressure and displacement fields are developed as independent variables. Finite-element solutions depend upon shape function and the numerical integration technique ; however, the suitable numerical condition for a laminated rubber bearing has not been fully discussed. The present study shows the mixed finite-element formulation in rate form for hyperelasticity, and show numerical examples of the laminated rubber bearing system in shear deformation in 2-dimensional as well as 3-dimensional case to clarify the advantage of the analysis method and the fundamental feature of mechanical response.