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1.
We consider the buckling of a simply supported plate subjected to a constant edge thrust λ. The aspect ratio l is such that the critical thrust (the first bifurcation point of the associated non-linear eigenvalue problem) is of multiplicity two. A study of the non-linear static problem indicates that there are nine possible equilibrium states. One of these corresponds to the unbuckled state while the remaining eight represent buckled states. A linear stability analysis and a calculation of the potential energy of each of the static solutions indicates that four of the solutions are stable and five are unstable. 相似文献
2.
The buckled states of rectangular plates 总被引:1,自引:0,他引:1
In this paper, based on the generalized variational principle of plates, the buckled states of rectangular plates under uniaxial compression are studied by use of the finite element method and the numerical analysis results under various boundary conditions are obtained by using the continuation calculation method. 相似文献
3.
In this paper, for a rectangular sandwich plate with edges simply supported and subjected to a constant compressive thrust
λ along two opposite edges; the secondary bifurcation points and the secondary buckled states that bifurcate from the primary
buckled states are determined by a perturbation method. These results are useful for their numerical calculation and can be
used to explain the phenomenon of “mode-jumping”.
Project Supported by National Natural Science Foundation of China. 相似文献
4.
In this paper, the axisymmetric buckled states of an annular sandwich plate (Reissner- type sandwich plate) with the clamped inner edge which is subjected to a uniform radial compressive thrust at the clamped outer edge are studied. Firstly, the basic equation of the buckled problem is derived. Secondly, the critical loads for some parameters are obtained by using the shooting method. Finally, we discuss the existence of the buckled states in the vicinity of the critical loads and obtain the asymptotic expansions of the buckled states. 相似文献
5.
Stuart S. Antman 《Archive for Rational Mechanics and Analysis》1990,110(2):103-117
This paper treats the axisymmetric buckling of nonlinearly elastic Cosserat plates, which can suffer thickness changes, as well as flexure, midplane extension, and shear. The governing equations are accordingly quite complicated. Nevertheless, it is shown that all solutions, bifurcating or not, have a simple, detailed nodal structure that distinguishes branches globally.This paper is dedicated to Bernard Coleman on the occasion of his sixtieth birthday 相似文献
6.
The nonlinear, forced, damped vibrations of simply-supported rectangular sandwich plates with a viscoelastic core are studied. The general, nonlinear dynamic equations of asymmetrical sandwich plates are derived using the virtual work principle. Damping is taken into account by modelling the viscoelastic core as a Voigt-Kelvin solid. The harmonic balance method is employed for solving the equations of motion. The influence of the thickness of the layers and material properties on the nonlinear response of the plates is studied. 相似文献
7.
In this paper,fundamental equations and boundary conditions of the nonlinearbending theory for a rectangular sandwicl plate with a soft core are derived by meansof the method of calculus of variations.Then the nonlinear bending for a simplysupported rectangular sandwich plate under the uniform lateral load is investigated byuse of the perturbation method and a quite accurate analytic solution is obtained. 相似文献
8.
周次青 《应用数学和力学(英文版)》1986,7(11):1063-1081
An analysis for the nonlinear bendings of unsymmetrically layered anisotropic rectangular plates subjected to combined edge tensions and lateral loading under verious supports is presented. The uniformly valid N-order asymptotic solutions of the transverse deflection and stress function are derived by the singular perturbation method offered in [1]. The present investigation may provide a simple and convenient method for such a complex problem. 相似文献
9.
周次青 《应用数学和力学(英文版)》1988,9(3):295-309
This paper has studied the nonlinear bending of symmetrically layered anisotropic rectangular plates under various supports.
The uniformlys valid N-order asymptotic solutions of the deflection and stress function are derived by the singular perturbation
methods offered in [1]. The analysis and calculations are given for simply and clamped supported, rectangular plates subjected
to combined edge tensions and lateral loading in conjunction with the modified Galerkin procedure (a method of weighted residuals). 相似文献
10.
A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective. 相似文献
11.
Geometrically nonlinear vibrations of FGM rectangular plates in thermal environments are investigated via multi-modal energy
approach. Both nonlinear first-order shear deformation theory and von Karman theory are used to model simply supported FGM
plates with movable edges. Using Lagrange equations of motion, the energy functional is reduced to a system of infinite nonlinear
ordinary differential equations with quadratic and cubic nonlinearities. A pseudo-arclength continuation and collocation scheme
is used and it is revealed that, in order to obtain the accurate natural frequency in thermal environments, an analysis based
on the full nonlinear model is unavoidable since the plate loses its original flat configuration due to thermal loads. The
effect of temperature variations as well as volume fraction exponent is discussed and it is illustrated that thermally deformed
FGM plates have stronger hardening behaviour; on the other hand, the effect of volume fraction exponent is not significant,
but modal interactions may rise in thermally deformed FGM plates that could not be seen in their undeformed isotropic counterparts.
Moreover, a bifurcation analysis is carried out using Gear’s backward differentiation formula (BDF); bifurcation diagrams
of Poincaré maps and maximum Lyapunov exponents are obtained in order to detect and classify bifurcations and complex nonlinear
dynamics. 相似文献
12.
Simplified nonlinear governing differential equations proposed by Berger for static cases and extended by Nash and Modeer for dynamic cases are used to analyse the title problem. Steady-state harmonic oscillations are assumed and the time variable is eliminated by a Kantorovich averaging method. The enclosure or comparison theorem of Collatz is then applied to the reduced equations to obtain the upper and lower bounds for the fundamental nonlinear frequency of simply-supported rectangular plates with linearly varying thickness. The fundamental eigenvalues are given for several taper and aspect ratios.Nomenclature
a, b
dimensions of plates
-
A
i
series coefficients
-
D
Eh
3/12(1–
2) flexural rigidity
-
D
0
Eh
0
3
/12(1–
2)
-
E
Young's modulus
-
h
thickness, h
0(1+x)
-
h
0
thickness parameter
-
N
x
, N
y
stress resultants in the X and Y directions
-
N
(N
x
+N
y
)/(1+)
-
P
1, P
2, ...
parameters
-
Q
1, Q
2, ...
parameters
-
R[X, (A/h
0)2]
bounding function
-
t
time
-
u, v
in-plane displacements
-
lateral deflections of plate
-
X=x/a
dimensionless co-ordinate
-
x, y
rectangular co-ordinates
-
y
n
(X)
series related to
-
thickness taper ratio
-
parameter in the neighbourhood of
-
error-function associated with differential equation
-
eigenvalue relating to frequency
-
Poisson's ra-tio
-
plate material specific weight
-
(X)
function related to plate deflection
-
(X)
admissible functions
-
circular frequency 相似文献
13.
14.
Nonlinear Dynamics - A new model-free robust control scheme for payload swing angle attenuation of two-dimensional crane systems with varying rope length is introduced in this work. The proposed... 相似文献
15.
Nonlinear bending of simply supported symmetric laminated cross-ply rectangular plates 总被引:4,自引:0,他引:4
Based on the von Kármán-type theory of plates,nonlinear bending problems of simplysupported symmetric laminated cross-ply rectangular plates under the combined action ofpressure and inplane load are investigated in this paper.The solution which satisfies thegoverning equations and boundary conditions is obtained by using the double Fourier seriesmethod. 相似文献
16.
周次青 《应用数学和力学(英文版)》1984,5(3):1383-1397
In this paper, the nonlinear bendings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement w and stress function are derived by the perturbation offered in [1]. 相似文献
17.
Shaukat Mirza 《Experimental Mechanics》1976,16(10):392-396
The present investigation deals with the stress distribution in the vicinity of rectangular inserts in finite rectangular plates. This problem is more complex due to the singularities at the corners of the inserts. In this paper, the finite-element technique is used to determine the deformations and, subsequently, the stresses. The paper treats the problem in a generalized form in the sense that the size and orientation of the insert are taken as variables. The finite rectangular plate is subjected to a uniform axial tensile load. The material of the plate and that of the insert are considered to be different. Element selections are made which are optimal with regard to accuracy and computational effort. The local element stresses which generate considerable discontinuity at the element nodes are plotted. Averaging process for the local stress calculations is discussed and these are compared with the results available1 which are obtained by experimental techniques. 相似文献
18.
Nonlinear response of a parametrically excited buckled beam 总被引:6,自引:0,他引:6
A nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented. The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using a digital computer and are compared with those obtained via an analog-computer simulation. The complicated dynamic behaviors that were found include period-multiplying and period-demultiplying bifurcations, period-three and period-six motions, jump phenomena, and chaos. In some cases, multiple periodic attractors coexist, and a chaotic attractor coexists with a periodic attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented. 相似文献
19.