Construction And Application Of Weak Form Quadatrure Beam Element For Reinforced Concrete

As a fundamental element, weak form quadrature beam element in previous studieshas demonstrated its advantages over the finite element. However, most of the previousstudies have been restricted to linear elastic materials, while the material nonlinearity isindispensable to practical engineering application. In fiber model, the relativelycomplex three-dimensional material constitutive relations are simplified intoone-dimensional uniaxial constitutive relation. The quadrature beam element iscombined with the fiber model to perform material nonlinearity analysis. Mander modeland Kent-Park model are used as concrete uniaxial constitutive model, while Légeronmodel is taken as steel uniaxial constitutive model.First of all, the quadrature beam element is used to simulate the static hysteresisprocess of reinforced concrete members and frames. The Newmark-β method is used toanalyze the structural dynamic time history response and results are compared withthose of OpenSees. The performance of the quadrature beam element is at least on a parwith that of the FEM in elastoplastic analysis of frames.Next, the quadrature element is also applied to analysis of bridge structures andconcrete diaphragm wall structures.The earthquake response of Chaolian interflow main viaduct is calculated with thequadrature beam element. As compared with MIDAS/Civil, the quadrature beamelement shows its effectiveness and high accuracy of results when dealing with beamsof complex variable cross-section. Furthermore, several examples are studied to showthe influence of element division on the accuracy of results.The diaphragm wall of Humen No.2Bridge is studied using the quadrature beamelement. Moreover, a defect in the model of the design code is revealed.Results of examples show that fewer elements are often needed in quadratureelement analysis. Although there are degrees-of-freedom at internal integration points inan element, they can be condensed out, lowering the amount of computation cost of theentire model. From the results of a few diaphragm wall examples, the computational advantagesof quadrature element are further verified, especially for diaphragm walls undernonlinearly distributed soil pressure.In the application of the quadrature element, some problems such as treatment ofcomplex boundary conditions and constraint equations have been encountered, to whichfurther research efforts are needed.