ANALYSIS OF THE LARGE DEFLECTION DYNAMIC PLASTIC RESPONSE OF SIMPLY-SUPPORTED CIRCULAR PLATES BY THE“MEMBRANE FACTOR METHOD”

Based on energy equilibrium,a new procedure called the Membrane Factor Method is devel- oped to analyze the dynamic plastic response of plates with deflections in the range where both bending mo- ments and membrane forces are important.The final deflection of a simply -supported circular rigid-plastic plate loaded by a uniformly distributed impulse is obtained.In comparison with other approximate solutions, the present results are found to be simpler and in better agreement with the corresponding experimental values reoorded by Florence.

Buckling and large deflection behaviors of radially functionally graded ring-stiffened circular plates with various boundary conditions

The buckling and large deflection behaviors of axis-symmetric radially functionally graded （RFG） ring-stiffened circular plates are investigated by the dynamic relaxation （DR） method combined with the finite difference discretization technique. The material properties of the constituent components of the RFG plate are assumed to vary continuously according to the Mori-Tanalka distribution along the radial direction. The nonlinear governing equations are obtained in the incremental form based on the firstorder shear deformation plate theory （FSDT） and the von Karman relations for large deflection. In the buckling analysis, an external in-plane load is applied to the plate in- crementally so that, in each load-step, the incremental form of the governing equations can be solved by a numerical code prepared based on the DR method. After converging the DR code in the first increment, the latter load-step is added to the previous one, and the program is repeated again. The critical buckling load is determined from the compressive load-displacement curve obtained by solving the incremental form of the governing equations. Based on the present incremental form of formulation, a bending analysis can also be conducted if the whole load is applied simultaneously. Finally, a detailed parametric study is carried out to investigate the influences of various boundary conditions, grading indices, thickness-to-radius ratios, stiffener＇s positions and depths on the critical buckling load, and displacements and stresses resulted from the bending analysis. It is observed that the effect of the stiffener on the results is much greater in the functionally graded plate with higher material grading indices. The results also reveal that, by increasing the depth of the stiffer, the values of ascending the critical buckling load are approximately identical for both simply supported and clamped boundary conditions.

Numerical Solution of Membrane Forces for A Free-Free Floating Plate with Large Deflection

Considering that the thickness of a pontoon-type very large floating structure (VLFS) is very small in comparison with the length and width, VLFS can be modeled as a thin plate. In theory, the displacements and the membrane forces of a plate with large deflection are all the functions of the second-order differentials of the Ariy stress function. With these characteristics considered, the Ariy stress function of a floating free-free plate is calculated by setting the virtual values of three of the corner points. The finite difference method is chosen to solve the problem. When the Ariy stress function of the plate is obtained, the membrane forces can easily be calculated. Comparisons between the forces induced by the membrane forces and by the fluid are considered. It is shown that the membrane forces can not be neglected in many cases.

PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORM TION OF LARGE AXISYMMETRICAL DEFLECTION(Ⅰ)--COUNTING NONLINEAR DEFORMATIONS OF RING SHELLS AND COMPRESSED ANGLE OF BELLOWS

This paper follows the work of[1,2].There are some progress in dealing with moderately small rotations(the squares of rotation angles are the order of magnitude of strains)of middle surface normals of inside and outside ring shells and compressed angle of bellows.Calculation results agree with experiments well.To bellow design,the method given in this paper is of practical value and the discussion of the influence of compressed angle on characteristic relation is helpful.

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

NONLINEAR FLEXURAL WAVES IN LARGE-DEFLECTION BEAMS

The equation of motion for a large-deflection beam in the Lagrangian description are derived using the coupling of flexural deformation and midplane stretching as a key source of nonlinearity and taking into account the transverse, axial and rotary inertia effects. Assuming a traveling wave solution, the nonlinear partial differential equations are then transformed into ordinary differential equations. Qualitative analysis indicates that the system can have either a homoclinic orbit or a heteroclinic orbit, depending on whether the rotary inertia effect is taken into account. Furthermore, exact periodic solutions of the nonlinear wave equations are obtained by means of the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function m→1 in the degenerate case, either a solitary wave solution or a shock wave solution can be obtained.

AN ANALYSIS OF THE LARGE DEFLECTION OF AN ELASTIC-PLASTIC CANTILEVER SUBJECTED TO AN INCLINED CONCENTRATED FORCE

Based on the Plastica theory (see ref. [12]), the large deflection of an elastic-perfectly plastic cantilever subjected to an inclined concentrated force at its tip, before the unloading in the plastic region occurs, is analyzed in this paper. The emphasis of the analysis is put on the effects of the angle of inclination of the concentrated force upon the deformed shape, the load-deflection relationship and the length of the plastic region. Both analytical and computed results are given.

NUMERICAL ANALYSIS OF THE LARGE DEFLECTION OF AN ELASTIC-PLASTIC BEAM

The layered approach was adopted to study the numerical procedure of the large deflection of art elastic-plastic Timoshenko' s beam, and the nonlinear equilibrium equation was derived by TL Formula. The solution was conducted by means of mNR method. The tangential stiffness matrix of the beam,vas introduced, and the solving procedures were presented in detail. The solution of the problem is satisfactory.

Analysis of Stability and Large Deflection Buckle of Rolled Strip by Third Power B-Spline Function Method

A new method——the third power B-spline function method is developed to analyse the stability and the buckle of rolled strip under residual stress.The large deflection theory of thin plate is used to calculate the buckle of rolled strip and criterion of critical buckle is given.The computed results tally with those of experiment well,which provides theoretical basis and method for developing the mathematical model of flatness control.

ANALYSIS OF THE LARGE DEFLECTION DYNAMIC RESPONSE OF RIGID-PLASTIC CIRCULAR PLATE RESTING ON FLUID

A study is presented for the large deflection dynamic response of rigid- plastic circular plate resting on potential fluid under a rectangular pressure pulse load. By virtue of Hankel integral transform technique,this interaction problem is reduced to a problem of dynamic plastic response of the plate in vacuum.The closed-form solutions are derived for both middle and high pressure loads by solving the equations of motion with the large deflection in the range where both bending moments and membrane forces are important.Some numerical results are given.

Large deflection of annular throttle-slices in shock absorbers

method was used to derive the stiffness curve equation of a single throttle-slice in shock absorbers. The analytical formula of large deflection for superposed throttle-slices was deduced directly and generalized. The undetermined coefficients of analytical for- mula were obtained through the finite element method （FEM） and curve fitting. Numerical results show that the analytical formula has satisfactory accuracy.

Comparison Between Two Solutions Based on the Relationship of Load-deflection Character of a Large Deflection Rubber Circular Plate

The rubber circular plate is considered as a kind of membrane. Based on the character that there exists no bending moment inside a membrane, the geometric behavior of the rubber circular plate in expanding state was described with the aid of a group of mathematic method. The relationship between deflection and load was attained by means of calculating stress and strain inside the curved surface of rubber plate. Meantime, based on Hencky method, the relationship between deflection and load was attained and considered as the Hencky solution. The different results given rise by the two different resolving methods were compared. The deviation results from the Hencky method was discussed, and a kind of correcting method was put forward.

Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes

This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates and panels using a finite element method.Based on the first-order shear deformation theory(FSDT),the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type.A C^0 isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite rotations.By adopting the extended rule of mixture,the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency parameters.Four carbon nanotube(CNT)distributions,labeled uniformly distributed(UD)-CNT,FG-VCNT,FG-O-CNT,and FG-X-CNT,are considered.The solution procedure is carried out via the Newton-Raphson incremental technique.Various numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present model.The effects of the CNT distributions,their volume fractions,and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.

A NEW TECHNIQUE FOR SOLVING NON-AXIALLY SYMMETRICALLARGE DEFLECTION OF ELASTIC AND THIN CIRCULAR PLATES

A new technique for solving large deflection problem of circular plates flexural non-axisymmetrically is proposed in this paper. The large deflection problem of a circular plate with built-in edge under non-axisymmetrical load is taken as an example to clarify the principle and procedure of the technique mentioned here. The technique given here can also be used to solve large deflection problem of circular plates under other non-axisymmetrical loads and boundary conditions.

SECOND ORDER APPROXIMATION SOLUTION OF NONLINEAR LARGE DEFLECTION PROBLEMS OF YONGJIANG RAILWAY BRIDGE IN NINGBO

The solution and computational aspects on nonlinear deflection of Yongjiang Railway Bridge in Ningbo were investigated. An approximate iteration algorithm on nonlinear governing equation was presented, and the obtained results show that, if altitude difference and span of the riverbanks are taken as 5 meters and 100 meters, respectively, the maximum gradient in the middle of the bridge exceeds 5%, much larger than maximum allowance gradient in railway design code. Therefore, a new solution scheme for decreasing gradient of the bridge is put forward, that is, the altitude difference between two riverbanks can be decreased to about 1/10 of the initial magnitude by building roadbeds with 0.5% gradient and 1 kilometer length at two riverbanks. As a direct result, the deflection gradient of the railway bridge is much reduced and the value is between 0.5% similar to 0.6%.

Large nonlinear deflection behavior of IPMC actuators analyzed with an electromechanical model

This study presents an electromechanical engineering model for the analysis of the large deflection curves of ionic polymer-metal composite(IPMC)cantilever actuators under direct current(DC)voltages.In this paper,the longitudinal normal strain performance of the material was investigated using digital image correlation on a micro-scale.The deflection of the actuator is analytically obtained with the application of an elliptic integration method based on the relationship between strain gradient and excitation voltage,and the minimum excitation voltage is derived based on the assumption that the actuators have small deformations.The validity of the electromechanical model is then justified with the experimental results obtained from Pt-and Ag-IPMC actuators at various excitation voltages.The findings of this study confirm that the introduced electromechanical model can accurately describe the large nonlinear deflection behavior of IPMC actuators.

BIPARAMETRIC PERTURBATION SOLUTIONS OF LARGE DEFLECTION PROBLEM OF CANTILEVER BEAMS

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach. This kind of substitution can transform the basic equation, an integral differential equation into nonlinear algebraic ones, thus simplify computational process. Compared with present results, it indicates that the large deflection problem solved by using pseudolinear analysis can lead to simple and precise results.

Large deflection of curved elastic beams made of Ludwick type material

The large deflection of an axially extensible curved beam with a rectangular cross-section is investigated. The elastic beam is assumed to satisfy the Euler-Bernoulli postulation and be made of the Ludwick type material. Through reasonably simplified integration, the strain and curvature of the axis of the beam are presented in implicit formulations. The governing equations involving both geometric and material nonlin- earities of the curved beam are derived and solved by the shooting method. When the initial curvature of the beam is zero, the curved beam is degenerated into a straight beam, and the predicted results obtained by the present model are consistent with those in the open literature. Numerical examples are further given for curved cantilever and simply supported beams, and the couplings between elongation and bending are found for the curved beams.

Dynamic plastic response of clamped stiffened plates with large deflection

Study on the dynamic response, and especially the nonlinear dynamic response of stiffened plates is complicated by their discontinuity and inhomogeneity. The finite element method (FEM) and the finite strip method are usually adopted in their analysis. Although many useful conclusions have been obtained, the computational cost is enormous. Based on some assumptions, the dynamic plastic response of clamped stiffened plates with large deflections was theoretically investigated herein by a singly symmetric beam model. Firstly, the deflection conditions that a plastic string must satisfy were obtained by the linearized moment-axial force interaction curve for singly symmetric cross sections and the associated plastic flow rule. Secondly, the possible motion mechanisms of the beam under different load intensity were analysed in detail. For structures with plastic deformations, a simplified method was then given that the arbitrary impact load can be replaced equivalently by a rectangular pulse. Finally, to confirm the validity of the proposed method, the dynamic plastic response of a one-way stiffened plate with four fully clamped edges was calculated. The theoretical results were in good agreement with those of FEM. It indicates that the present calculation model is easy and feasible, and the equivalent substitution of load almost has no influence on the final deflection.

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.