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nonlinear bending OF CORRUGATED DIAPHRAGM WITH LARGE BOUNDARY CORRUGATION UNDER COMPOUND LOAD

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Applied Mathematics and Mechanics(English Edition) 2003年第4期24卷 414-420页

作者：袁鸿刘人怀 FacultyofConstruction GuangdongUniversityofTechnology InstituteofAppliedMechanics JinanUniversity

By using the simplified Reissner's equation of axisymmetric shells of revolution, the nonlinear bending of a corrugated annular plate with a large boundary corrugation and a nondeformable rigid body at the center under compound load are investigated. The nonlinear boundary value problem of the corrugated diaphragm reduces to the nonlinear integral equations by applying the method of Green's function. To solve the integral equations, a so_called interpolated parameter important to prevent divergence is introduced into the iterative format. Computation shows that when loads are small, any value of interpolated parameter can assure the convergence of iteration. Interpolated parameter equal or almost equal to 1 yields a faster convergence rate; when loads are large, interpolated parameter cannot be taken too large in order to assure convergence. The characteristic curves of the corrugated diaphragm for different load combinations are given. The obtained characteristic curves are available for reference to design. It can be concluded that the deflection is larger when the diaphragm is acted by both uniform load and concentrated load than when it is acted only by uniform load. The solution method can be applied to corrugated shells of arbitrary diametral sections.

关键词： corrugated diaphragm large boundary corrugation nonlinear bending elastic characteristic annular plate

nonlinear bending OF SIMPLY SUPPORTED SYMMETRIC LAMINATED CROSS-PLY RECTANGULAR PLATES

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Applied Mathematics and Mechanics(English Edition) 1990年第9期11卷 801-807页

作者：刘人怀何陵辉 Shanghai University of Technology Shanghai Shanghai Institute of Applied Mathematics and Mechanics Shanghai

Based on the von Karman-type theory of plates, nonlinear bending problems of simply supported symmetric laminated cross-ply rectangular plates under the combined action of pressure and inplane load are investigated in this paper. The solution which satisfies the governing equations and boundary conditions is obtained by using the double Fourier series method.

关键词： laminated rectangular plate nonlinear bending governing equation

nonlinear thermo-structural behavior of sandwich panels with truss cores under through-thickness gradient temperature field

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Theoretical & Applied Mechanics Letters 2018年第3期8卷 184-192页

作者： Wu Yuan Hongwei Song Chenguang Huang Key Laboratory for Mechanics in Fluid Solid Coupling Systems Institute of Mechanics Chinese Academy of Sciences School of Engineering Science University of Chinese Academy of Sciences

A theoretical analysis is presented to predict the nonlinear thermo-structural response of metallicsandwich panels with truss cores under through-thickness gradient temperature field, which is acommon service condition for metallic thermal protection system （TPS）. The in-planetemperature distribution is assumed to be uniform, and through-thickness temperature field isdetermined by heat conduction. Two typical conditions are analyzed： nonlinear thermal bendingin fixed inside surface temperature, and thermal post-buckling in fixed temperature differencebetween two surfaces. Temperature-dependent mechanical properties are considered, andgradient shear stiffness and bending stiffness due to non-uniform temperature is included. Resultsindicate that the temperature-dependent material properties obviously affect bending resistance;however, the effect is negligible on post-buckling behavior. Influences of geometric parameters onthe thermo-structural behavior of the sandwich panel according to the present theoretical modelare discussed.

关键词： Sandwich panel with truss core Thermal protection system Thermo-structural response nonlinear bending Post-buckling

bending of simply-supported circular timber beam strengthened with fiber reinforced polymer

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Applied Mathematics and Mechanics(English Edition) 2014年第3期35卷 297-310页

作者：杨骁杨峥文群 Department of Civil Engineering Shanghai University

The bending behavior of the circular cross-section timber beam strengthened with a fiber reinforced polymer(FRP) sheet is investigated. The tight bonding is on the interface between the surface of a timber beam and the reinforcement layer of the FRP sheet. An analytical expression for the bending moment-curvature relation is presented, and its failure modes are analyzed. The governing equation for nonlinear small deflection of the FRP-strengthened circular timber beam is established, and the corresponding numerical method is given. The bending deformation of the simply-supported circular timber beam strengthened with the carbon fiber reinforced polymer(CFRP) sheet subject to a uniform load is studied numerically. The influence of the angle and thickness of the CFRP layer as well as the timber strength on the bending deflection of the FRPstrengthened circular timber beam is examined. It is revealed that, with the increases of the thickness and angle, the deflection of the CFRP-strengthened circular timber beam is decreased, and its carrying capacity and ductility are increased. However, when the angle of the layer reaches a certain value, the deflection will no longer decrease with the increase of the angle. At the same time, the nonlinear bending moment-curvature relation of the CFRP-strengthened circular timber beam is simplified as an approximate bilinear constitutive model. The approximate deflections of the simply-supported circular timber beam strengthened with the CFRP sheet are obtained. The results are compared with the linearly elastic bending and nonlinear bending models, showing that the mid-span deflections of a CFRP-strengthened circular timber beam with the approximate bilinear constitutive model are greater than those with the nonlinear constitutive model. The results of its stiffness analysis are on the safe side.

关键词： fiber reinforced polymer(FRP) reinforcement circular timber beam nonlinear bending bending moment-curvature relation failure mode

METHOD OF GREEN’S FUNCTION OF CORRUGATED SHELLS

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Applied Mathematics and Mechanics(English Edition) 2005年第7期26卷 830-837页

作者：袁鸿张湘伟 Institute of Applied Mechanics Jinan University Guangzhou 510632 P.R.China Faculty of Construction Guangdong University of Technology Guangzhou 510640 P.R.China

By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was *** results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.

关键词： corrugated shell Green's function integral equation nonlinear bending elastic characteristic

EFFECT OF TRANSVERSE SHEAR ON FINITE DEFORMATION OF GENERALLY LAMINATED SHALLOW SHELL WITH DOUBLE CURVATURE

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Acta Mechanica Solida Sinica 1996年第1期9卷 27-41页

作者： David Shikao Chia Ford Motor Company DearbornMichigan 48121USA

nonlinear equations of equilibrium for the titled shell of rectangular planform under transverse and inplane edge loads are derived by using the virtual work principle and expressed in terms of a stress function,the transverse displacement and two rotation *** sheU is elastically re- strained against rotation.A generalized double Fourier series solution is formulated for nonlinear bending of the *** Galerkin technique furnishes an infinite set of simultaneous nonlinear alge- braic equations for the above four variables,which can be truncated to obtain any desired degree of ac- *** results for antisymmetrically laminated angle-ply and cross-ply graphite-epoxy doubly curved panels are presented graphically for the transverse shear effect and various shell parame- ters and boundary *** present results are also compared with available data.

关键词： nonlinear bending transverse shear doubly curved shaUow shell laminate