NONLINEAR BENDING THEORY OF DIAGONAL SQUARE PYRAMID RETICULATED SHALLOW SHELLS

Double-deck reticulated shells are a main form of large space structures. One of the shells is the diagonal square pyramid reticulated shallow shell, whose its upper and lower faces bear most of the load but its core is comparatively flexible. According to its geometrical and mechanical characteristics, the diagonal square pyramid reticulated shallow shell is treated as a shallow sandwich shell on the basis of three basic assumptions. Its constitutive relations are analyzed from the point of view of energy and internal force equivalence. Basic equations of the geometrically nonlinear bending theory of the diagonal square pyramid reticulated shallow shell are established by means of the virtual work principle.

Non-Linear Vibration of Rectangular Reticulated Shallow Shell Structures

This paper deals with non-linear vibration of rectangular reticulated shallow shells by applying non-linear elastic theory of such structures established by the author .Us-ing the assumed (generalized)Fourier series solutions for transverse deflection (latticejoint transverse displacement )and force function,weighted means of the trial functions lead to the relations among the coefficients related to the solutions and vibration equ-ation which determines the unknown time function,and then the amplitude -frequeney relations for free vibration and forced vibration due to harmonic force are derived withthe aid of the regular perturbation method and Galerkin procedure,respectively.Nu-merical examples are given as well.

ANALYTICAL FORMULAS OF SOLUTIONS OF GEOMETRICALLY NONLINEAR EQUATIONS OF AXISYMMETRIC PLATES AND SHALLOW SHELLS

Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equa- tions.

A MODIFIED HELLINGER-REISSNER VARIATIONAL FUNCTIONAL INCLUDING ONLY TWO INDEPENDENT VARIABLES FOR LARGE DISPLACEMENT OF THIN SHALLOW SHELL

The variational functional of the Hellinger-Reissner variational principle for the large displacement problem of a thin shallow shell with an arbitrary shape is first established. Then the functional of the modified principle suitable for the finite element method is derived. In the functional only two independent variables, the deflection w and the stress function F are included. The displacement expressions in the middle surface on the boundary of the shell is also derived by means of the previous two variables.

UNIQUENESS FOR THE SOLUTIONS OF ELASTIC THIN PLATES AND SHALLOW SHELLS AS WELL AS THEIR CONTACT PROBLEM WITH HALF SPACE

The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the second.

SNAP-BUCKLING OF DISHED SHALLOW SHELLS UNDERUNIFORM LOADS

A theoretical analysis is presented for the snap-buckling behaviour of dished shallow shells under uniform loads. By means of the modified iteration method the second approximate formula of elastic behaviour. and a set of numerical solutions are given. And effects of parameters beta and k on the snap-buckling behaviour are discussed.

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITSAPPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

This paper applied the simplified theory.for multilayer sandwich shells undergoingmoderate small rotations in Ref [1] to shallow shells. The equilibrium equations andboundary conditions of large deflction of orthotropic and the special case. isotropicshells, are presented.

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION(III)──LARGE DEFLECTION AND POSTBUCKLING OF SHALLOW SHELLS

In this paper, exact solutions of large deflection of multilayer sandwich shallow shellsunder transverse forces and different boundary conditions are presented. Exact results ofpostbuckling of multilayer sandwich plates, shallow cylindrical shells and nonlineardeflection of general shallow shells such as spherical shells under inplane edge forcesare also obtained by the same procedure.

SNAP-BUCKLING OF DISHED SHALLOW SHELLS UNDER LINE LOADS

A theoretical analysis is presented for the snap-buckling behavior of dished shallow shells under axisymmetric distributed line loads. The second approximate formula of elastic behavior of dished shallow shells with various boundary conditions are given, and effects of geometrical parameters gamma, beta and k on non-linear behavior are discussed.

Nonlinear thermo-mechanical stability of eccentrically stiffened functionally graded material sandwich doubly curved shallow shells with general sigmoid law and power law according to third-order shear deformation theory

In this paper, the nonlinear analysis of stability of functionally graded ma- terial （FGM） sandwich doubly curved shallow shells is studied under thermo-mechanical loads with material properties obeying the general sigmoid law and power law of four ma- terial models. Shells are reinforced by the FGM stiffeners and rest on elastic foundations. Theoretical formulations are derived by the third-order shear deformation theory （TSDT） with the von Karman-type nonlinearity taking into account the initial geometrical im- perfection and smeared stiffener technique. The explicit expressions for determining the critical buckling load and the post-buckling mechanical and thermal load-deflection curves are obtained by the Galerkin method. Two iterative algorithms are presented. The effects of the stiffeners, the thermal element, the distribution law of material, the initial imper- fection, the foundation, and the geometrical parameters on buckling and post-buckling of shells are investigated.

Nonlinear Analysis and Optimization of Shallow Shells of Variable Thickness

This paper is concerned with the nonlillear bending, stability and optimal design of revolution shallowshells with variable thickness. The problems are investigated by means of a modified iterative method proposedearlier by the author. Solutiolls for nonlinear bedding and stability problems of revolution shallow shells withvariable thickness, such as spherical and conical shells, are presented. Deflections and critical loads for stability arecalculated and the numerical results are plotted and given in tabular forms. It is showil that the equation determiningthe maximum deflection and the load coincides with the cusp catastrophe manifold. The optimal design of plates andshells, in Which the volullle is minimized or the critical load of shells is maximized, is investigated. When the volumeoftlle shell and the arch height of the shell are given, the variable thickness parameter can be solved. In addition, thispaper also gives tile constraint optimization of nonlinear bedding of circular plates.

Dynamic Properties of Viscoelastic Open Shallow Shells

On the basis of the Kármán Donnell theory of thin shells with large deflections and the Boltzmann laws for linear viscoelastic materials, the mathematical model for viscoelastic open shallow shells was formulated. By using the Galerkin average method, the original integro partial differential dynamic system was simplified as a integro ordinary differential dynamic system, which can be transformed into a ordinary differential dynamic system by introducing new variables. The dynamical behavior was studied by some classical methods. Dynamical properties, such as, chaos, strange attractor, limit cycle etc., were discovered.

NONLINEAR FREE VIBRATION OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION UNDER THE STATIC LOADS

In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.

NONLINEAR VIBRATIONS OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION

A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.

Numerical Simulation Study on the Surface Deflection of Cylindrical Shallow Shell

The increasing applications of new materials such as high strength low alloy (HSAL) steels and aluminum alloy sheets have lead to greater focus on the surface deflections of auto body panels in the automobile industry in recent years.The finite element models of cylindrical shallow shell that can represent auto body panels are established.Numerical simulations of forming and unloading of cylindrical shallow shell are carried out.And a measurement and evaluation method of the surface deflection is introduced.The simulations of surface deflections with various blank homing forces (BHF) show great agreement with the experi- mental results.The influence laws of sheet thickness and material properties such as yield strengthσs,strain-hardening exponent n,anisotropy parameter r and strength coefficient k on the surface deflection are achieved by simulations,which give a basic refer- ence for controlling surface deflections.

Global Existence and Uniqueness of Weak Solution to Nonlinear Viscoelastic Full Marguerre-von Kármán Shallow Shell Equations

By Galerkin finite element method, we show the global existence and uniqueness of weak solution to the nonlinear viscoelastic full Marguerre-von Karman shallow shell equations.

Exact internal controllability for shallow shells

The internal control problem is considered, based on the linear displacement equations of shallow shell. It is shown, with some checkable geometric conditions on control region, that the undergoing shallow shell is exactly controllable by using Hilbert uniqueness method （HUM）, piecewise multiplier method and Riemannian geometry method. Then some examples are given to show the assumed geometric conditions.

SNAP－THROUGH OF LAMINATED ORTHOTROPIC SHALLOW SPHERICAL IMPERFECT SHELLS WITH TRANSVERSE SHEAR

The equations of large deformations of laminated orthotropic spherical shellsare derived. The effects of transverse shear deformation and initial imperfection are considered. on this basis. the semi-analytical solution of the axisymrnetric snap-throughbuckling of laminated orthotropic shallow spherical shells under uniform pressure is obtained using orthogonal collocation method. The effects of material parameters, structuralparameters, initial imperfection and transverse shear deformation are discussed.

THE ANALYSIS OF INTERLAMINAR STRESSES FOR COMPOSITE LAMINATED SHALLOW SHELLS WITH INTERFACIAL DAMAGE

Based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis and nonlinear theory of shallow shells, considering the damage effect of the interlaminar in- terface and using the variation principle, the three-dimensional non-linear equilibrium differential equations of the laminated shallow shells with interfacial damage are derived. Then, considering a simply supported laminated shallow shell with damage and under normal load, an analytical solution is presented by using finite difference method to obtain the interlaminar stresses. Numer- ical results show, the stiffness of the shell is weakened, greater absolute values of displacements as well as smaller interlaminar stresses are obtained by interfacial damage. When the interfacial damage is further increased, delamination occurs obviously under normal pulling load and pure shear slip occurs under normal pressure load. The portion of the load undertaken by the two sides of the interface is more different. Different mechanical behaviors are shown in both sides of the interface, and the discontinuation of stresses and displacements takes place in the interface.

ITERATIVE METHOD FOR LARGE DEFLECTION NONLINEAR PROBLEM OF LAMINATED COMPOSITE SHALLOW SHELLS AND PLATES

Based on the results by Wang,in this paper, the iterative method is presented for the study of large deflection nonlinear problem of laminated composite shallow shells and plates. The rectangular laminated composite shallow shells have been analyzed. The results have been compared with the small deflection linear analytical solution and finite element nonlinear solution. The results proved that the solution coincide with small deflection linear analytical solution in the condition of the low loads and finite element nonlinear solution in the condition of the high loads.