Determination of buckling mode and explicit expression of critical load for simply supported rectangular orthotropic plates under biaxial compression

1988 ◽  
Vol 9 (9) ◽  
pp. 907-913
Author(s):  
Li Shu-guang
Keyword(s):  
Critical Load ◽  
Explicit Expression ◽  
Biaxial Compression ◽  
Orthotropic Plates ◽  
Buckling Mode ◽  
Simply Supported

Determination of the zeros of a cross-product Bessel function

1973 ◽  
Vol 74 (3) ◽  
pp. 477-483 ◽  
Author(s):  
L. Z. Salchev ◽  
V. B. Popov
Keyword(s):  
Critical Load ◽  
Real Number ◽  
Power Law ◽  
Bessel Functions ◽  
Cross Product ◽  
Positive Parameter ◽  
Inertia Moment ◽  
Simply Supported ◽  
Image Position

In many mechanical and other problems the following equationis reached, where Jν(α) and Yν(α) are Bessel functions of the first and second kind of any real order ν and β is a positive parameter.For example, equation (1) is reached in the case of determining the critical load Pcr, for a simply supported strut with a variable inertia moment by a power law, where the power m is any real number.

Post-Buckling Behaviour of Rectangular Orthotropic Plates

1973 ◽  
Vol 15 (1) ◽  
pp. 25-33 ◽  
Author(s):  
M. K. Prabhakara ◽  
C. Y. Chia
Keyword(s):  
Large Deflection ◽  
Double Series ◽  
Double Fourier Series ◽  
Biaxial Compression ◽  
Orthotropic Plates ◽  
Good Convergence ◽  
Simply Supported ◽  
Rectangular Orthotropic Plate ◽  
Post Buckling ◽  
Transverse Deflection

An analysis is presented for the post-buckling behaviour of a simply supported, rectangular, orthotropic plate subjected to biaxial compression. The solution of von Karman-type large deflection equations of the plate satisfying the prescribed boundary conditions is expressed in the form of a double Fourier series for the transverse deflection and a double series for the stress function consisting of the appropriate beam functions. The effect of plate properties on stresses and deflections has been studied for three fibre-reinforced materials. Numerical results indicate good convergence of the present series solution and are compared with the available data.

Closed-Form Critical Buckling Load of Simply Supported Orthotropic Plates and Verification

2019 ◽  
Vol 19 (12) ◽  
pp. 1950157 ◽  
Author(s):  
Zhao Jing ◽  
Qin Sun ◽  
Ke Liang ◽  
Jianqiao Chen
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Buckling Load ◽  
Coupling Coefficients ◽  
Orthotropic Plates ◽  
Buckling Mode ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Torsional Coupling

The buckling mode is important to determine the critical load of specially orthotropic rectangular plates under axial compression with simply supported boundary. However, in classical laminated plate theory (CLPT), the critical buckling mode can only be obtained by iterative or numerical methods. This paper derives the critical buckling mode mathematically and presents the critical buckling load in closed form. By taking advantage of the derived closed-form solution, it is convenient to investigate the effects of aspect ratio, load ratio, and fiber orientation on the buckling load, and the parameters affecting the buckling mode can be easily obtained. The first-order shear deformation theory (FSDT)-based finite element method is developed to verify the closed-form solution. The bending-torsional coupling effects are analyzed and discussed to assess the approximation of the buckling behavior of specially orthotropic plates to general laminates. The obtained finite element solutions of general laminates are compared with the closed-form solutions of specially orthotropic plates. The accuracy of approximation of the buckling behavior of specially orthotropic plates to the general laminates increases as the bending-torsional coupling coefficients decrease. The closed-form solution can be applied to laminates with small bending-torsional coupling coefficients.

Stiffness compensation through matching buckling loads in a compliant four-bar mechanism

2021 ◽  
pp. 1-23
Author(s):  
Armin Numic ◽  
Thijs Blad ◽  
Fred van Keulen
Keyword(s):  
Critical Load ◽  
Strain Energy ◽  
Buckling Mode ◽  
Buckling Loads ◽  
Simply Supported ◽  
Load Matching ◽  
Motion Range ◽  
Four Bar Linkage ◽  
Torsion Springs ◽  
Linkage Model

Abstract In this paper a novel alternative method of stiffness compensation in buckled mechanisms is investigated. This method involves the use of critical load matching, i.e. matching the first two buckling loads of a mechanism. An analytical simply supported four-bar linkage model consisting of three rigid links and four torsion springs in the joints is proposed for the analysis of this method. It is found that the first two buckling loads are exactly equal when the two outer springs are three times stiffer than the two inner springs. The force-deflection characteristic of this linkage architecture showed statically balanced behavior in both symmetric and asymmetric actuation. Using modal analysis, it was shown that the sum of the decomposed strain energy per buckling mode is constant throughout the motion range for this architecture. An equivalent lumped-compliant four-bar mechanism is designed; finite element and experimental analysis showed near zero actuation forces, verifying that critical load matching may be used to achieve significant stiffness compensation in buckled mechanisms.

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

Theoretical Determination of Rigidity Properties of Orthogonally Stiffened Plates

1956 ◽  
Vol 23 (1) ◽  
pp. 15-20
Author(s):  
N. J. Huffington
Keyword(s):  
Elastic Constants ◽  
Orthotropic Plate ◽  
Constant Thickness ◽  
Stiffened Plates ◽  
Geometrical Configuration ◽  
Orthotropic Plates ◽  
Theoretical Determination

Abstract The analysis of bending and buckling of orthogonally stiffened plates may be simplified by conceptually replacing the plate-stiffener combination by an “equivalent” homogeneous orthotropic plate of constant thickness. This procedure requires the determination of the four elastic rigidity constants which occur in the theory of thin orthotropic plates. Methods are presented whereby these quantities may be determined analytically in terms of the elastic constants and geometrical configuration of the component parts of the structure.

scholarly journals State space approach with FEM for the determination of structural behaviour of composite plates

2017 ◽  
Vol 8 (4) ◽  
pp. 468-483
Author(s):  
Asad Shukri Albostami ◽  
Zhangjian Wu ◽  
Zhenmin Zou
Keyword(s):  
Plate Thickness ◽  
Composite Plates ◽  
Thickness Direction ◽  
Middle Plane ◽  
Structural Behaviour ◽  
State Space Approach ◽  
Content Type ◽  
Simply Supported ◽  
Space Approach

Purpose An analytical investigation has been carried out for a simply supported rectangular plate with two different loading conditions by using 3D state space approach (SSA). Also, the accurate location of the neutral plane (N.P.) through the thickness of the plate can be identified: the N.P. is shifted away from the middle plane according to the loading condition. The paper aims to discuss these issues. Design/methodology/approach SSA and finite element method are used for the determination of structural behaviour of simply supported orthotropic composite plates under different types of loading. The numerical results from a finite element model developed in ABAQUS. Findings The effect of the plate thickness on displacements and stresses is described quantitatively. It is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant. Originality/value This paper describe the effect of the plate thickness on displacements and stresses quantitatively by using an exact solution called SSA. Also, it is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant.

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