Study On An Elastic Conjugate Shell With Optimal Relationship Between Structure Shape And Stress State

The shell belongs to the space stressed system and it is favored by people because of its large span,strong bearing capacity and beautiful appearance.Generally speaking,plates are considered as bending members,while shells are considered as compression members.This is just hope that there is only compressive stress and no bending moment on the cross section of shell plate when the shell undergoes elastic deformation under the design load,i.e.,the shell is expected to have the optimal structural morphology.But the shells designed by the existing design methods usually have bending moment or even tensile stress.So,researchers propose to use the experimental method of hanging flexible materials to create the initial shape of the shell with the optimal structural morphology,i.e.,the so-called physical reverse hanging method.However,the physical reverse hanging method is not suitable for the generation of the initial shape of the shell with large rise span ratio due to the limitation of elastic deformation ability of materials.Therefore,the problem of optimal structural morphology creation and structural design of shell are investigated in this thesis,and an analytical method for generating the initial shape of elastic shell with the optimal structural morphology and a conjugate method for designing this kind of elastic shell are proposed.The shell designed by the conjugate design method is hereinafter referred to as the conjugate shell.The main contents of this thesis are as follows.(1)Based on the mirror deformation between the axial tension deformation of membrane and the axial compression deformation of shell under uniformly-distributed transverse load,an analytical method is proposed to create the initial shape of elastic shell with optimal structural morphology by referring to the idea of physical inverse hanging method.By constructing the conjugate effect in the mirror deformation of membrane and shell,the analytical solution of conjugate shell is derived by using the analytical solution of the super large deflection problem of membrane,and the conjugate method for designing the elastic shell with optimal structural morphology is proposed.(2)The basic equations used in the existing membrane problems are improved,and the problem of transverse uniformly-distributed loaded circular membrane is analytically dealt with.Thus,the key problem of the initial shape generation and conjugate design of the circular conjugate shell is solved.By improving the out-of-plane equilibrium equation,in-plane equilibrium equation and geometric equation used in the existing membrane problems,the governing equations for the super large deflection problem of the circular membrane are established.The power series method is used to solve the governing equations,and the analytical solution of this circular membrane problem is presented.The static loading experiment of circular membrane is also carried out,and the results show that the analytical solution is basically reliable.(3)By using the conjugate design method and the analytical solution of the circular membrane problem,the design theory of circular conjugate shell is established.It mainly involves the initial shape generation,design of shell plate and edge member,stability checking and natural frequency of circular conjugate shell.The analytical solution of the super large deflection problem of circular membrane is used to calculate the deformed shape of the circular membrane which is used to generate the initial shape of circular conjugate shell.Based on the conjugate effect in the mirror deformation of plate and shell,the analytical solution of conjugate shell used in the section design and reinforcement calculation of shell plate and edge member are derived by using the analytical solution of circular membrane.The maximum curvature radius of the circular conjugate shell is calculated,and the stability of the conjugate shell is checked by using the formula of circular shell given in the current regulation.After cutting the circular conjugate shell with variable curvature into many segments and treating each segment of the shell as a conical shell,the governing equations of free vibration of the conical shell are established based on D'Alembert's principle and thin shell theory and solved by using Galerkin method,and finally the natural frequency of the circular conjugate shell is obtained by using boundary conditions and continuity conditions.The results of parameter discussion show that: under the same rise span ratio,the initial shape of circular conjugate shell is independent of the elastic modulus and thickness of shell,but it will contract inward with the increase of Poisson's ratio;the natural frequency of the conjugate shell increases nonlinearly and the increasing rate gradually slows down with the increase of the rise of shell.(4)The experimental research and finite element analysis of the circular conjugate shell were conducted to verify the advantage of the structural morphology of conjugate shell and some related contents of the conjugate design theory.A rotary forming device of shell was developed,and cement mortar shells of conjugate shell and conventional shells with the same rise and span are made.The results of the static loading experiment show that the conjugate shell has higher load carrying capacity compared with conventional shells.Three groups of shells with different rise span ratios(there are three kinds of shells with different initial shapes in each group,and each kind of shell has three specimens)are fabricated by 3D printing.Static loading and free vibration experiments are conducted to verify the validity of analytical solution and the calculation formula of the natural frequency of shell in conjugate design theory.In addition,finite element models of conjugate shells with different rise span ratio are established,and the response of conjugate shell under non-uniform loads are analyzed.