Modelling Damage, Fragmentation and Progressive Collapse of Structures Using Gausian Springs Based Applied Element Method - Mai Abdul Latif (2018)
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 col-lapse 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 ma-terial 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 loca-tion 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 modiﬁca-tion, 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 ex-act 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 Gaus-sian AEM is performed on 2D frames subject to earthquake loads and extreme wind loads.