This investigation is to develop a numerical model suitable for nonlinear analysis of reinforced concrete shells. A nine-node Lagrangian element Figure (1) with enhanced shear interpolation will be used in this study. Table (1) describes shape functions and their derivatives of this element. An assumed transverse shear strain is used in the formulation of this element to overcome shear locking. Degenerated quadratic thick plate elements employing a layered discrelization through the thickness will be adopted. Different numbers of layers for different thickness can be used per element. A number of layers between (6 and 10) have proved to be appropriate to represent the nonlinear material behavior in structures. In this research 8 layers will be adequate. Material nonlinearities due to cracking of concrete, plastic flow or crushing of concrete in compression and yield condition of reinforcing steel are considered. The maximum tensile strength is used as a criterion for crack initiation. Attention is given to the tension stiffening phenomenon and the degrading effect of cracking on the compressive and shear strength of concrete. Perfect bond between concrete and steel is assumed. Attention is given also to geometric nonlinearities. An example have been chosen in order to demonstrate the suitability of the models by comparing the predicted behaviour with the experimental results for shell exhibiting various modes of failure.

In this study the nonlinear transient dynamic analysis of reinforced concrete slabs using the finite element method is presented. Eight-node Serendipity degenerated elements have been employed. This element is based on isoparametric principles with modifications, which relax excessive constraints. The modifications include reduced order integration to overcome the shear locking. A layered approach is adopted to discretize the concrete through the thickness. Both an elastic-perfectly plastic and strain hardening plasticity approaches have been employed to model the compressive behavior of the concrete. A tensile strength criterion is used to initiation of crack and a smeared fixed crack approach is used to model the behavior of the cracked concrete. Tension stiffening in concrete is assumed such that the concrete can take some tension after cracking. Implicit Newmark with corrector-predictor algorithm is employed for time integration of the equation of motion. Several examples are analyzed using the proposed model. The numerical results showed good agreement with other sources.