变分与有限元大作业_图文.doc

Finite Element Stress Analysis of a Square Plate Containing a Hole under the uniaxial tensile loading on two opposite edges A Computer Project Report by 王狄辉（SX1501082） May,2016 Catlog Chapter 1 Description of the Problem 1 Chapter 2 Finite element model 2 2.1 Geometry Model 2 2.2 Meshing 2 2.3 Boundary Condition 3 Chapter 3 Results and Discussions 4 3.1 Displacements 4 3.2 Stress Tensor 5 3.3 Stress Concentrate Factors 7 Chapter 4 Concluding Remarks 10 Chapter 1 Description of the Problem A square plate containing one hole is under the uniaxial tensile loading on two opposite edges, as shown in Fig. 1.1. The value of presented in Fig. 1.1 equals to 2mm when ’s value equals to 1mm. The values of and W are all 80/60/40/20/10 mm. The material of the plate is Aluminum whose elasticity modulus =70GPa and Poisson ratio is 0.33. And the inclusion material is steel whose elasticity modulus =206GPa and Poisson ratio is 0.28. The thickness of the plate is 0.1mm. Fig. 1.1 Sketch of the plate In this report, plots for distributions of displacements u v and plots for distributions of three stress components will be found. It will also be found that the table of stress concentrate factors at points A, B, C, D and their variation of H/a. Chapter 2 Finite element model 2.1 Geometry Model Because both the plate and the load are double symmetry, this report would use a quarter model for FEM calculation. Using commercial software CATIA to model the plate which is shown in Fig. 2.1. Fig. 2.1 The quarter model of plate 2.2 Meshing The commercial software Hypermesh was used to mesh the model in Chapter 2.1. Elements used are 12-DOFs triangular elements, as is shown in Fig. 2.2. Due to the stress concentration around the edge of the plate and the inclusion, the elements around the edge are more than elements in the other part of the model. Fig. 2.2 Meshing of the model 2.3 Boundary Condition For that a quarter model instead of a whole model was used, those two symmetry axis