A modified direct stiffness method for finite element model reduction - Peng, Chongtian (2019)
With the wide applications of Finite Element Analysis, Model Reduction Methods become necessary to reduce the model size and thereby the computational resources needed, especially for complex finite element models. The common drawback of the Model Reduction Methods is the existence of error which is inversely proportional to the size of reduced model produced. That to say, the simpler the reduced model, the higher the error. Thereby, the pursuit of new methods or alternatives to reduce errors remain as a goal, in the finite element analysis of complex engineering problems. This Final Year Project (FYP) report deals with the development of a new method of Finite Element Model Reduction as an alternate way of achieving the reduced model. Instead of the usual continuous functions used in finite element literature, a discretized version of shape functions, called the ‘shape vectors’, is used in this method. The new method of model reduction developed in this FYP is called “Modified Direct Stiffness Method” in view of its similarity with the well-known Direct Stiffness Method. It is tested using a simple bar/beam/shaft model to check its feasibility and efficacy. The results obtained are encouraging. Further research is needed to improve the accuracy of the proposed method.