Static and dynamic analysis of linear elastic systems on non-prismatic three dimensional beam elements

Bibliography: leaves 100-103.A computer programme NONPRI, has been developed for the analysis of three dimensional skeletal assemblages consisting of non-prismatic members. It is capable of static and dynamic analysis of structures consisting of members whose constitutive relationship is linear elastic. The finite element formulation is based on the family of quadratic isoparametric finite elements. The three noded space frame element is quite versatile in that it can account for shear as well as flexural 9 axial and torsional deformation effects making it suitable for thin and thick beam analysis and for cases where the axial and torsional deformations are relevant. The element can be degenerated to a truss/frame transition element (3 translational degrees of freedom at each node - rotations ignored) and further degenerated to become a truss element. Furthermore, the element internal node is defined to lie at an arbitrary position inside the element. Thus, this flexibility in the non-prismatic element formulation makes it very powerful in practical analysis problems. An out-of-core solution technique is used for the equations of static analysis bearing in mind the capability for solving large structural systems. An in-core solution technique is used for the equations of dynamic analysis bearing now in mind that these equations represent an iterative process which can otherwise become computationally very expensive

Constitutive modelling and finite element analysis in geomechanics

Bibliography: pages 208-222.The major objective of the work presented in this thesis was the development of a constitutive model for hard rock at high pressure. The model should capture the important features of material behaviour and should be soundly based on mechanical principles; furthermore it should be simple enough to permit implementation and use in large general purpose finite element codes. As a preliminary exercise, a state-of-the-art plasticity cap model was developed in order to provide a basis for comparison with the new model. Existing cap models were shown to exhibit certain inconsistencies associated with the suppression of a regime of potentially unstable behaviour; these inconsistencies were identified and eliminated in. the formulation which is presented in this thesis. The new rock model was based on internal damage concepts. The model is isotropic, and internal damage is measured by a scalar damage parameter. The properties of the material degrade as the damag~ parameter increases, and an evolution law governs the rate at which damage occurs. The damage model was calibrated against experimental results for Bushveld Norite, which is a very hard, brittle rock. The general form of the model, however, is suitable for application to soil and concrete. Both the plasticity cap model and the damage model were implemented into the finite element code NOSTRUM (developed by the Applied Mechanics Research Unit at the University of Cape Town). Solutions of a series of boundary value problems, including typical mining excavation problems, are presented to illustrate and compare the models