Research On The Computional Model And Method Of Plate Structures And The Complex Soil In The Safety Analysis Of Nuclear Power Structures

Based on the National Natural Science Foundation of China and the entrusted project from the China research and development department of EDF,the dynamic interaction between the nuclear power plant and the complex soil is analyzed in this paper.In the interaction analysis,the key work is to simulate the soil and superstructures,which can improve the accuracy and efficiency of the computation.The soil always presents to be layered in the long term of the formation process.In addition,surveys and experiments find that the great differences of physical and mechanical properties occur in the horizontal and vertical direction and the soil is anisotropic.In order to solve the interaction between the structure and soil precisely,the characters of nonhomogeneity and anisotropy must be considered.Until now,some effective models and numerical methods have been developed by researchers.But the accuracy and efficiency are always limited.By virtue of the precise integration method and dual vectors,a newly refined multi-layered model is proposed in the paper.Using the proposed approach,the static and dynamic response of the anisotropic and stratified soil is solved precisely.The superstructure of the nuclear power plant is mainly comprised of plates,shells and other entity structures.The static and dynamic response of plates is also analyzed in this paper to improve the reliability of the nuclear safety evaluation.Built on the scaled boundary finite element method,a highly efficient and precise plate model is presented.Making use of this method,precise results can be obtained.Because of the similar research thinking and methods,the interdisciplinary problems are also solved in this paper.The static and dynamic response of layered piezoelectric materials and magneto-electric-elastic plates is analyzed and some meaningful results are gained.The main research contents and acquired achievements in the paper are in the following:1.As to the static and dynamic response of the multi-layered soil under loads,the mixed variable method of the layered soil is further developed in this paper.In this method,the governing partial differential equations are converted into the second order ordinary differential equation with the help of the Hankel integral transform.Utilizing the dual vectors,the second order ordinary differential equation is simplified as a first order ordinary differential matrix equation.The precise integration method is applied to solve the first order ordinary differential equation and results in the frequency-wave number domain are obtained.Using the inversion of the Hankel transform,solutions in the frequency-physical domain can be acquired.Numerical examples demonstrate that the proposed approach is accurate and can be applied to various transversely isotropic multilayered soil.2.Based on the scaled boundary finite element method,a model for the orthotropic plate is developed.The model can solve the problem of thin plates,thick plates and laminated composite plates.The model is built on two-dimensional meshes and higher order elements are applied to discretize the plate,which contributes to improving the efficiency and accuracy.The displacements in three directions are considered as the basic variables to derive the key equations.The displacement and stress field in the thickness direction can be solved analytically.The derivation is based on basic equations of the three dimensional elastic theory.The governing equation of the scaled boundary finite element method is a second order ordinary differential matrix equation which can be converted into a first order homogeneous linear ordinary differential matrix equation.The solution to the first order ordinary differential equation is a matrix exponential function.The exponential function is solved by the precise integration method and any desired accuracy can be accomplished.Numerical examples illustrate that displacements,normal and transverse stresses obtained by the proposed method are in good agreement with exact solutions of the three dimensional elastic theory.3.The free vibration problem of plates is considered.Similar with the derivation of the plate bending problem using the scaled boundary finite element method,the dynamic governing equations of plates are presented.Making use of dual vectors and the Pade expansion,the dynamic stiffness matrix is acquired.From the dynamic stiffness matrix,the static stiffness matrix and mass matrix are gained and the free vibration problem of plates is solved.Numerical examples show that the natural frequencies of single layer plates and laminated composite plates from this method are highly accurate.4.Through combining the stiffness matrix of plates and the modulus of the Winkler soil based on the scaled boundary finite element method,the interaction between the plate and Winkler soil is solved.According to the principle of the freedom matching,the stiffness matrix of the multi-layered soil and plates is combined together to analyze the response of the system constituted by the plate and layered soil.5.Utilizing the precise integration method,the static and dynamic response of layered piezoelectric materials is studied.Beginning with the governing equations of motion and the constitutive equations of the piezoelectric material,and with the help of the Hankel transform and dual vectors,a first order ordinary differential matrix equation is obtained,which can be solved by the precise integration method.Results of displacements,electric potential,stresses and electric displacements in the frequency-wave number domain are acquired.Both mechanical and electrical quantities of the piezoelectric material in the frequency-physical domain can be gained by taking the inversion of the Hankel integral transform.6.Solutions of a magneto-electro-elastic plate are acquired by applying the scaled boundary finite element method.In the whole process,the detailed derivation is based on the three-dimensional governing equation.By means of the scaled boundary coordinates and the principle of virtual work,a second order ordinary differential equation of the scaled boundary finite element method is acquired.Taking advantage of the nodal force,the second order ordinary differential equation is converted into a first order ordinary differential equation.Its general solution is a matrix exponential which is solved by the Pade series expansion.Finally,solutions of elastic displacements,electric potential,magnetic potential,stresses,electric displacements and magnetic induction vectors in the magneto-electro-elastic plate are gained.