Nonlinear time-dependent seismic response of unanchored liquid storage tanks

The present study investigates the effects of liquid hydrodynamic pressures exerted on thin-walled liquid storage tanks during earthquake motions. Several complexities are involved in the analysis of such tanks depending on their boundary conditions. In the case of unanchored liquid storage tanks, complexities arise due to successive contact and separation between base plates and foundations, large amplitude deformations of base plates, pre- and post-buckling behavior of shells, material yielding, soil-tank interaction, and large-amplitude free surface sloshing.; The main objective of this research is to develop a two/three dimensional computer model capable of performing simulation of the complex dynamic behavior of various types of liquid storage tanks subjected to a strong seismic base excitation. The model takes into consideration both large amplitude liquid sloshing and nonlinear liquid-structure interaction using the finite element method. The program also has the following features: (1) An up-to-date finite element technology for the analysis of solids and curved shells using the degeneration concept, and considering material plasticity and geometric nonlinearity. The program is expandable to accommodate any desired new plastic model. (2) Modeling of potential flow problems using an efficient Eulerian finite element. (3) Modeling of free surface sloshing that utilizes the nonlinear wave theory formulation. The updated Lagrangian description of the liquid domain boundaries is utilized to keep track of the free surface position at any time. (4) A variational principle that forms the basis for the numerical discretization of nonlinear fully coupled liquid-structure interaction problems with free surface sloshing. Since a Lagrangian description of the solid motion is utilized, the program uses an updated Eulerian-Lagrangian description of the liquid-solid interface in order to enforce compatibility between solid and liquid elements. The resulting nonlinear Euler-Lagrange equations are solved using an efficient time integration technique that has been specially developed to solve the liquid-structure interaction problems. (5) General contact analysis that accommodates a wide range of contact problems including liquid-structure interaction problems. A Lagrange multiplier technique was employed to enforce both displacement compatibility and force transmissibility constraints along unknown contact surfaces. The program efficiently handles the special case of contact of unanchored liquid storage tanks.