FINITE ELEMENT DYNAMIC ANALYSIS OF AXISYMMETRIC STRUCTURES

Abstract

In recent years analysis of axisymmetric structures, such as hyperbolic cooling towers, chimneys, reactor containment shells, etc., subjected to dynamic or seismic loading has attracted considerable attention, specially in the area of nuclear power plants. The structural safety of such structures during expected earthquake motion is of great importance in view of possibility of radiation hazards. Therefore, such structures are required to be analyzed and designed in most rational manner. Further due to rapid expansion in number and size of power plants in India and elsewhere in the world , there is great need for careful and detailed investigation of their behaviour under severe ground motions. In many countries, little consideration has been given to seismic forces in the design of structures because of infrequent occurrence of earthquakes in the past history. However, the potential damage exposure from an accident from a large power plant makes it imperative that ground motion effects be considered in the design of such structures, even in the areas that now appear to have low seismic activity. These important structures should not show any kind of distress under most severe motion expected in the life of the structure. The design philosophy of these structures differ from that of conventional buildings. The conventional structures are designed to be ductile permitting inelastic deformations and some damages are accepted while in these important structures the system should behave elastically during the seismic event. An axisymmetric structure resting on rock/soil subjected to an earthquake motions will develop additional stresses on the structure due to inertia effects. In general when a structure such as massive structure is embedded, it will interact with the surrounding and base soil. The dynamic analysis of such structures involve consideration of several aspects such as characteristics of ground motion and its frequency content, soil structure interaction effect, energy dissipating characteristics of structure and foundation. The dynamic analysis of axisymmetric structures has been studied by many investigators in the past but many aspects like modelling of boundaries, modelling of reactor internals along with complete reactor building has not received sufficient attention with particular reference to reactor type containment structures. In this thesis, study has been made of the problems which are encountered in the seismic analysis of massive embedded axisymmetric structures subjected to strong ground motions. The seismic response of two axisymmetric structures, that is, (i) Containment shell and (ii) Intake tower has been studied using beam and finite element methods of analysis considering the soil-structure interaction effects. The beam model does not represent real behaviour of soil-structure system because of one-dimensional idealization. To capture the real behaviour of soil-structure system subjected to horizontal ground motions, three-dimensional modelling of the system is required. The axisymmetric finite element method takes into account 3-dimensional nature of the system and is employed to carry out a detailed investigation of some of the aspects of dynamic analysis of axisymmetric structures. The soil is assumed to be linearly elastic and its damping is higher as compared to that of structure. Asingle value of damping has been assigned to each mode which reflects both the low damping of the structure and the high damping of the soil. This has been done by calculating a weighted damping based on strain energy in various sub systems including soil. The dimensions of the structure are finite while the soil mass around the structure is of infinite extent in horizontal and vertical directions. So the approximate dimensions of the soil are to be determined for dynamic analysis of soil-structure system. To do so, a parametric study of depth and width of soil has been done for the containment structure subjected to horizontal ground motion. The effect of considering soil mass on the seismic response of structure has also been studied. Two massive embedded axisymmetric structures, containment shell alone and the complete reactor building with internals are analyzed by finite element model to study the effect of soil-structure interaction on overall seismic response of the structure. These two structures with fixed base, and flexible base of different shear wave velocities of soil are subjected -to horizontal ground motion and responses are computed. The responses of these structures fixed at base are compared to that of structures founded on soil having different elasticity properties. Also the effect of depth of embedment of these two structure on seismic behaviour of soil-structure system has been investigated. In order to study the effect of the characteristics of ground motion on these two structures, three real earthquake motions are normalized to common peak accelerations and elastic time history analysis has been carried out for containment and reactor building. The structural behaviour of reactor building during earthquake is explained with the aid of mode shapes of the structure. The six component of stresses are obtained from seismic analysis of a reactor building and are plotted along the height of outer shell. This showed that the stress pattern is significantly changed at the junction points such as junction of shell and raft. The finite element seismic analysis of some axisymmetric structures has been carried out using timewise mode superposition and direct step-by-step time integration methods. The choice of one method over the other has been determined by studying seismic response of these structures. The fixed soil boundaries in finite element mesh of soil-structure system under seismic event reflect the incoming waves and affect the response of the structure. In order to absorb the incoming waves and minimize their reflection at the boundary, the viscous boundaries in the form of dampers are employed . A study has been carried out to evaluate the effectiveness of these viscous boundaries in absorption of most of the incoming waves in relation to fixed boundaries. Also, study is made to determine the position of placing viscous boundaries in horizontal and vertical directions of soil medium. Even with the sophisticated finite element analysis of reactor building, the reactor internal being non-axisymmetric poses problems in its axisymmetric idealization. The various methods of modelling of reactor internals as equivalent axisymmetric body are employed. The two hypothetical reactor buildings of different size and type are selected and their internals are modelled by using various modelling methods. The seismic response of these two reactor buildings with their equivalent internal structure has been computed and examined. The study is made to determine the suitable method of modelling of internals for obtaining more realistic seismic response of a reactor building.