Theory Investigation Of New Computational Methods For Engineering Thermal Analysis

The heat transfer and related thermal-mechanical analyses are of great importance for the design and manufacture of structures in most practical engineering problems. As the analytical solutions of these problems are not available, numerical methods are employed for the analyses. There are mainly two types of numerical methods, the finite element method and the meshless method. Due to low accuracy and computational capability, the traditional finite element method has difficulty in solving these problems, when using lower order elements. The traditional meshless method has problems of complex computational process and lower efficiency as well. However, these lower order elements have great advantage when generating the background meshes. The Approximation of complex geometrical characteristic is very simple when using the triangular element or tetrahedral element and the related mesh generation algorithm is also very simple. This advantage will be more obvious especially in the thermal analyses of complex problems.In order to deal with thermal engineering problems more efficiently, several lower order thermal-mechanical elements are proposed in this paper, based on the weakened weak form and generalized gradient smoothing technique. Plenty of numerical examples are given to test the accuracy and convergence rate of proposed elements. It is proven that these elements can be utilized to solve complex thermal engineering problems, and they also have great advantage when generating the background meshes. The main work includes the following details:1. Triangular or tetrahedral thermal-mechanical elements based on gradient smoothing technique are proposed for the analyses of thermal engineering problems. The gradient smoothing technique is combined with traditional finite element method and the solution procedure of two-dimensional thermal problems is presented. This method calculates the numerical integration in those edge-based smoothing domains, which can soften the numerical model efficiently. Therefore, the accuracy is greatly improved. New materials and structures used in practical engineering are discussed in this paper. Plenty of linear and nonlinear analyses are carried out. Moreover, the face-based smoothed technique is further formulated for the three-dimensional heat transfer and related thermal-mechanical analyses. This method calculates the numerical integration in those face-based smoothing domains, instead of the element domains. The accuracy is also improved and there are no additional parameters or degrees of freedom. This method can be utilized conveniently to solve three-dimensional thermal engineering problems, especially when the geometry or the boundary conditions are complex.2. A cell-based smoothing radial point interpolation method is extended for heat transfer and related thermal-mechanical problems. The shape function is constructed using the polynomial basis directly and has the property of Kronecker8function, therefore the essential boundary condition can be applied accurately. In this method, the triangular or tetrahedral meshes are further divided into several smoothing cells. The supporting node selection is incorporated with the meshless interpolation plan. Then, the supporting node selection and integration plan are given based on these obtained smoothing cells. Due to high accuracy and convergence rate, this method has good performance when dealing with thermal engineering problems. This method can also deal with the mesh distortion effectively and it can give accurate solutions even when the mesh quality is very poor. This method can overcome the defect of the traditional meshless method, when dealing with the analyses of thermal engineering problems.3. An edge-based smoothed thermal-mechanical triangular shell element is proposed for the implicit analyses. The quadratic interpolation method is used along the thickness direction of shell element, when dealing with the heat transfer analysis. This element can provide higher accuracy and can give the distribution of temperature filed of any location along the thickness direction of shell element. The present element can be easily derived from the existing triangular shell elements with little changes. The proposed element has good accuracy and is not sensitive to mesh distortion, which is very useful for the thermal engineering analysis.4. The proposed edge-based smoothed thermal-mechanical triangular shell element is utilized to simulate the hot stamping process of high strength steel. The nodal internal force, external force and inertial force for the explicit analyses are obtained using the weakened-weak form. A general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is also presented. The obtained numerical results are compared with the experimental results. It can be found that the proposed element can be utilized efficiently for the complex dynamic large deformation analysis of coupled multi-field problems.