Improved Meshless Method For The Solution Of Temperature Field And Thermal Stress And Its Application To Hydraulic Structure Analysis

Temperature field and thermal stress are often encountered in the construction and running periods of mass concrete structures, which are throughout the whole life cycle of mass concrete structures. From the cement hydration heat during the early concrete casting to the cycle changes of air temperature and water temperature during the running period, they have a significant impact on temperature field and thermal stress of mass concrete structures. The cement hydration heat dissipates quickly during the early concrete casting, and resulting thermal stress may lead to cracks in the concrete, which seriously damages structure integrity of concrete structure and endangers structure safety. Hence concrete delaminating and blocking casting are needed in the construction of the mass concrete structures and necessary temperature control measures should be adopted such as decreasing casting temperature, adopting pipe cooling. Climatic conditions, material properties, running environmental conditions and so on can affect thermal stress of mass concrete structures.so that the stress state of structure is influenced. Thermal stress can be classified into uncoupled and coupled thermal stress. Most of the hydraulic structure thermal stress belongs to uncoupled thermal stress, which means temperature field is computed firstly and thermal stress analysis according to the temperature follows. The coupled effect between them need not to be considered.Meshless method is a newly approved numerical method, in which the problem domain and domain boundaries are only discretized by nodes. Due to its getting grid of the mesh, even if scattered nodes distribution can get good results, and meanwhile pre-processing and post-processing efforts can be saved greatly. The moving least squares (MLS) method is the mostly used in the shape function construction, but it is difficult to enforce the essential boundary conditions since shape functions constructed by the MLS approximation lack Kronecker Delta property. Here meshless method based on the moving Kriging (MK) interpolation is used for the solution of temperature field and thermal stress and applied to hydraulic structure analysis.Meshless method can be classified into the domain-type and boundary-type. Here the domain-type meshless method is used to solve continuous and discontinuous finite field thermal stress problems. The coupled thermal stress computation is considered in the continuous finite field thermal stress analysis. In the discontinuous finite field thermal stress computation, the newly extended element-free Galerkin method (XEFG) is proposed in the frame of MK interpolation. While for the boundary-type meshless method, the newly EFG-SBM is proposed by combining EFG with the scaled boundary equation in the frame of MK interpolation. EFG-SBM possesses the advantages of EFG and scaled boundary finite element method (SBFEM). Here EFG-SBM is applied to solve thermal stress of mass concrete structures considering the infinite field. The scaled boundary finite element method is a semi-analytical method for solving partial differential equations, in which only the boundary is discretized by finite element method and the problem fundamental solution is not needed. It is more advantageous and convenient than boundary element method. It has advantage in solving infinite domain and stress singularity problems. The major content of the dissertation is organized as follows:(1) Meshless local Petrov-Galerkin (MLPG) method based on the MK interpolation is used to solve the finite field uncoupled and coupled thermal stress problems. For uncoupled thermal stress, transient heat conduction analysis is computed firstly. MLPG can achieve higher accuracy compared to finite element method through scattered nodes distribution. Here nonlinear heat conduction analysis is also considered in which the thermal conductivity varies linearly with temperature. The importance of the thermal stress is illustrated by thermal stress computation of Fengman gravity dam during the running period finally. MLPG based on the MK interpolation is developed for the dynamic coupled thermoelastic analysis under thermal shock loading. The solution of differential equation is improved in this paper. The main idea of this method is based on the reduction procedure of the original system of PDEs describing coupled thermo-mechanical behavior to a system of second-order ordinary differential algebraic equations, which is solved by the standard Newmark time-integration scheme to obtain the numerical temperature and displacement field directly. There is no need for inverse Laplace transformation, so that the solving process is simplified greatly. In coupled thermal stress analysis, the effect of the coupled term is considered for temperature, displacement and stress. The conclusion "the effect of the coupled term to stress is actually similar to a damper" is verified. This solution method is also advantageous for the uncoupled thermal stress analysis.(2) The discontinuity thermal stress in the finite field can be divided into strong discontinuity problem (fracture problem) and weak discontinuity (material discontinuity problem). The newly extended element-free Galerkin (XEFG) method is proposed in the frame of MK interpolation. Because MK interpolation satisfies Kronecker Delta property, it is more convenient in enforcing the essential boundary conditions than the MLS-based XEFG method. Here the XEFG method based on the MK interpolation is applied to analyse temperature field and thermal stress of discontinuity in the finite field. XEFG method is a newly numerical method in which the MK interpolation is combined with extended finite element method (XFEM), and it inherits advantage of dealing with discontinuous media of XFEM.(3) The newly boundary-type meshless method which is called EFG-SBM is proposed by combining EFG with the scaled boundary equation in the frame of MK interpolation. Because MK interpolation satisfies Kronecker Delta property, it is more convenient in enforcing the essential boundary conditions than the MLS-based EFG-SBM. This new numerical method possesses the advantages of EFG and scaled boundary finite element method (SBFEM). Nodes distribution is only needed in the domain boundaries and the domain discretization is not necessary, so that the preprocessing and postprocessing are simplified in EFG-SBM. The numerical solutions show that the new method has higher computational accuracy and better convergence than SBFEM. Here EFG-SBM based on the MK interpolation is applied to solve thermal stress of mass concrete structures considering the infinite field. The influence of foundation on temperature field and thermal stress of the gravity dam is illustrated by analysing temperature field and thermal stress of Fengman gravity dam during the steady running period.