Three-dimensional Nonlinear Finite Element Analysis Of Reinforced Concrete Slabs

The nonlinear analysis of reinforced concrete slabs includes the ultimate load analysis and the finite element analysis. The ultimate load analysis, mainly the yield-line theory and strip method, cannot illustrate the development of inner forces, deflection or the spreading of the cracks. Meanwhile, the implementation of FEM can give the information. The usual FEM analysis for reinforced concrete slabs is to make use of the so-called layered models, in which slab is divided into a serious of layers. In the layered model, transverse shear is ignored and material is assumed to be in a state of plane stress, and some other presuppositions are introduced, such as cracking of concrete takes place only in the plane perpendicular to the normal. The introduction of these presuppositions are not real and may result in wrong resolutions by ignoring some dangerous situations. The present thesis attempts to implement a nonlinear FEM analysis by using 8-noded isoparametric brick element with equivalent reinforcement membrane. The main work carried out goes as following:(1) The stiffness matrix of the 8-noded isoperimetric brick element with equivalent reinforcement membrane is carefully deduced. Among all types of available three-dimensional nonlinear constitutive models, the nonlinear elastic constitutive models are chosen for the analysis of slabs subjected to monotonous loading. In the thesis, Bathe's nonlinear elastic constitutive model is modified to avoid iterative calculation in updating constitutive model. Non-tension method and smeared crack model is applied to the analysis of concrete cracking.(2) To cut down great calculation of assembling and disassembling of stiffness matrix in the nonlinear procedure, the initial stress method is introduced to resolve the nonlinear equations. The criteria of convergence and Gaussian integral rules are discussed as they affect the efficiency and precision of calculation.(3) A large computer program, named 3DPLATE, is developed with FORTRAN Powerstation . With 3DPLATE, 6 simply supported square plates. 5 clamped rectangular plates and 1 corner-supported plate are analyzed. The computational load versus deflection curves agree with the test results. And some useful strain curves and stress curves are illustrated.(4) Finally, the advantages and disadvantages of nonlinear analysis of reinforcedconcrete slabs with three dimensional element are discussed. And some suggestions on the implementation of brick element in plates analysis are given.