Research On Calculation Theory And Application Of Homogenization Conversion Of Functionally Graded Cylindrical Shells

In recent years,functionally graded cylindrical shell(FGM)has been widely used in the fields of aerospace,submersibles,chemical industry,communications and engineering.The corresponding theoretical research has also become a hot spot,and various countries have invested considerable scientific research funds to support.The work of this paper is part of the research content of the projects funded by the National Natural Science Foundation of China and the Henan Science and Technology Research Fund.This article is mainly to study the similarity of mechanical behavior between FGM cylindrical shells and homogeneous material cylindrical shells,and use the results obtained to solve their practical engineering application problems,so as to achieve the purpose of solving the FGM cylindrical shell problems with the familiar theory of homogeneous material cylindrical shells.After analyzing and comparing with reference data,it is verified that the method in this paper is accurate and effective,and the application is convenient,and it is suitable for engineering application promotion.The working conditions of the FGM cylindrical shell under various conditions of use are analyzed and discussed,and some meaningful laws are drawn to guide theoretical research and engineering applications.The thesis first reviews the current research status of homogeneous material cylindrical shells at home and abroad,summarizes and summarizes the theoretical methods,hydrostatic pressure,and ribbed cylindrical shells from various perspectives,and provides background materials for the development of FGM cylindrical shells.The second step is a brief introduction to the birth,advantages,and scope of application of FGM materials.Then the application field of FGM cylindrical shell is systematically explained the current research situation at home and abroad,especially in the theoretical research.Finally,the purpose and significance of the research in this article are put forward.The second part of the article points out that because the material properties of FGM cylindrical shells continuously change in the thickness direction,they exhibit different characteristics from the uniform material cylindrical shells,which makes the mechanical behavior analysis of FGM cylindrical shells more complicated than the corresponding uniform material cylindrical shells.However,the theoretical analysis method of the two materials can be consistent,and therefore the mechanical behavior can be compared and analyzed.Aiming at the similarity between FGM material and homogeneous material in mathematical and mechanical models,the two materials are closely related through mathematical and physical methods,revealing the inherent relationship between them,and realizing the "homogenization" conversion calculation of the macro-mechanical behavior of FGM cylindrical shells.After "homogenizing" the mechanical behavior of the FGM cylindrical shell,the tedious mathematical processing is avoided,and the calculation is simplified.At the same time,it can ensure sufficient calculation accuracy,reveal the common characteristics and laws of the mechanical behavior of FGM cylindrical shells theoretically,and provide a new exploration way for the analysis of the macroscopic mechanical behavior of FGM cylindrical shells.The third part is based on the first-order classic thin shell theory of Flügge and Love,using the wave method as the vibration displacement function.Through analysis and comparison to find the similar relationship between the FGM cylindrical shell and the uniform material cylindrical shell in the mathematical model,the natural frequency of the FGM cylindrical shell is converted into the uniform material solution under the same geometric size,boundary conditions and load conditions,so as to realize the homogenization of functionally graded materials.This method uses a relatively simple solution to the mechanics problem of a uniform material cylindrical shell to obtain a relatively complex solution to the mechanics problem of the FGM cylindrical shell.It avoids solving boundary problems of complex partial differential equations and provides convenient formulas for engineering applications.Finally,a calculation example is carried out to analyze the various parameters that affect the natural frequency of the FGM cylindrical shell in the vacuum,and the rules are summarized.The fourth part of the article uses the similar relationship between the mechanics and mathematical models of the FGM cylindrical shell and the homogeneous material cylindrical shell under hydrostatic pressure,and uses the classic Flügge shell theory to solve the natural frequency problem of the free vibration of the FGM cylindrical shell under hydrostatic pressure.At the same time,a solution to the critical pressure of FGM cylindrical shells under hydrostatic pressure is given,which provides theoretical support for non-destructive testing of FGM cylindrical shells.Through actual calculation examples,the geometric and physical parameters that affect the performance of FGM cylindrical shells under hydrostatic pressure are analyzed and summarized,the regular change curve is drawn,and the experience is summarized.The fifth part analyzes the vibration characteristics of the ribbed cylindrical shell by studying the classical shell Flügge theory and Donnell thin shell theory.Taking into account the rotational inertia of the shell and the movement of the ribs in and out of its plane and applying the homogenization theory,the wave method and the energy method are used to derive the vibration characteristic equations of the underwater stiffened functionally graded cylindrical shell.MATLAB is used to solve the characteristic equation to obtain the natural frequency of the stiffened cylindrical shell.The calculation example analyzes the variation law of natural frequency of circumferential and longitudinally ribbed functionally graded cylindrical shells under hydrostatic pressure with different shell size,material composition,circumferential and longitudinal rib section aspect ratio and rib spacing.The sixth part is that the stress intensity factor at the crack tip of the homogeneous material with cracks is an important parameter for the safety of the cracked components.Based on the research on the homogenization of FGM thin cylindrical shells in the previous parts,it explores the similar ratio relationship between the crack tip stress and the stress intensity factor between the FGM cylinder and the homogeneous material cylinder.A high-precision and fast calculation method for the stress intensity factor of FGM cylinders with annular cracks is proposed.Comparing the calculation results with the calculation results of reference documents,the feasibility and superiority of the method in this paper are verified.The last part summarizes and prospects the research content of this paper,and puts forward innovation points.