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Title: Modelling damage, fragmentation and progressive collapse of structures using Gausian springs based Applied Element Method
Author: Abdul Latif, Mai
ISNI:       0000 0004 7657 7340
Awarding Body: Swansea University
Current Institution: Swansea University
Date of Award: 2018
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Modelling the progressive collapse of structures is necessary for planning con-trolled demolitions, studying the effect of natural disasters on structures, and determining the weakest locations of a structure for further reinforcement and enhancement. Computational mechanics served an important contribution to modelling the progressive collapse of structures, since it is very expensive to model collapse in an experimental evaluation for large scales. Existing developments of computational methods for the scope of collapse of structures are extensively reviewed first. It is concluded that the Applied Element Method (AEM) is one of the simplest schemes for modelling the progressive collapse with sufficient accuracy. The AEM is represented as pairs of rigid elements connected by shear and normal springs, along the edges of the elements. The material properties are represented in the stiffness of the springs. The stresses and deflection between elements are based on the deflection of the springs. The deflection and internal stresses of several structural beams are assessed using the conventional AEM and it is evident that the computational efficiency of the method is inadequate since a sizable amount of elements and springs per element is required to achieve a specific level of accuracy. Hence, a modification to the AEM is necessary to reduce the computational cost of the method. This thesis is focused on the development of the AEM for linear and nonlinear material behaviour, the development of a damage material model for representing damage and fragmentation, and an application of collapse of structures subject to earthquake and extreme wind loading. The AEM is enhanced using the Gaussian quadrature to find the exact location of springs. Using a Gaussian distribution it is concluded that only 2 springs per element are required for elastic elements, while a total of 6 springs are required for elasto-plastic elements. In conjunction with the Gaussian springs modification, a further modification is implemented that utilises an adaptive technique for selecting the number of springs per element based on elasticity and elasto-plasticity of the springs. In nonlinear material analysis the Newton-Raphson integration scheme is adapted. To model damage in materials a softening material behaviour is employed. The developed softening algorithm is a return mapping method that is based on the predictor-corrector hardening plasticity algorithm. To represent the failure of a spring in the AEM, the stiffness of the spring is set to zero. This results in a singular global stiffness matrix that can not be solved directly. Using a dynamic model for the analysis eliminates the need of inverting the stiffness matrix, so the explicit Central Difference Method is used for linear and nonlinear dynamic analysis. The findings in this thesis are (1) the conventional AEM is modified by changing the distribution of the springs using the Gaussian quadrature allowing for exact calculation of optimal spring locations; (2) only 2 and 6 linear and nonlinear springs are needed, respectively between a pair of elements, reducing the overall computational cost of the structure and increasing the accuracy; (3) an adaptive transition springs technique is implemented and allowed for an overall reduced computational cost; (4) a softening return mapping algorithm is developed for representing material damage; (5) a time integrating technique is required when element separation occurs to avoid a singular matrix; (6) application of the Gaussian AEM is performed on 2D frames subject to earthquake loads and extreme wind loads.
Supervisor: Feng, Yuntian T. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral