Maximization of buckling load of laminated composite plates with central circular holes using MFD method

This paper addresses optimal design of simply supported symmetrically laminated composite plates with central circular holes. The design objective is the maximization of the buckling load, and the design variable is considered as the fiber orientation. The first-order shear deformation theory is used for the finite element analysis. The study is complicated because the effects of bending–twisting coupling are also included for the buckling optimization. The modified feasible direction method is used to solve the optimization problems. Finally, the effect of different number of layers, boundary conditions, width-to-thickness ratio, plate aspect ratios, hole daimeter-to-width ratio, and load ratios on the results is investigated.     

Elasto-plastic buckling of stiffener plates in beam-to-column flange connections

The problem of plastic buckling of steel plates is reviewed in relation to the load carrying capacity of stiffener plates in beam-to-column flange connections. Due to the non-uniformity of the stress distribution in these plates, the finite element method is used to compute the stresses in the elastic and plastic ranges. A bifurcation analysis is performed using both flow and deformation theory to evaluate the elasto-plastic buckling of the stiffener. A scaled inverse iterative version of the power method is employed to evaluate the bifurcation load. A parametric study is conducted on stiffeners and design curves are obtained showing the relationship between the critical stress and the slenderness ratio for different plate aspect ratios.     

Elastic buckling of tapered circular plates

This paper is concerned with the elastic buckling of tapered circular plates. The study is prompted by the fact that results hitherto available are restricted to a narrow range of taper parameters and are somewhat different from each other. For the buckling analysis, a simple and yet accurate numerical method is presented. It is based on the shooting method and the Rayleigh-Ritz approach. Comprehensive generic buckling results of circular plates with linearly and parabolically varying thicknesses are generated. Comparison studies of the buckling results showed that some of the existing results were erroneous. Optimal values of taper parameters for such tapered plates are also given.     

Thermal buckling of circular plates with localized axisymmetric damages

Thermal buckling analysis of circular plates with localized axisymmetric damages has been carried out using the finite element method. The damages are characterized as degradation in material properties locally. Thermal buckling load parameters are evaluated for both simply supported and clamped circular plates with varying locations, magnitudes and lengths of damage. Numerical results are presented for different cases, and trends in variations of load parameters are discussed.     

Axisymmetric buckling of bimodulus thick circular plates

The static buckling of bimodulus thick circular and annular plates subjected to a combination of a pure bending stress and compressive stress is investigated. The thick finite element model, which includes the effect of transverse shear deformation, are created for axisymmetric buckling problems. The obtained results of buckling coefficient are compared with the exact solutions for ordinary thin plates. The accuracy of the finite element solutions are shown to be very good. The effects of various parameters on the buckling coefficients and neutral surfce locations are studied. The bimodulus properties are shown to have significant influences on the buckling coefficient.     

Axisymmetric snap buckling of imperfect, tapered circular plates

The application of the Dynamic Relaxation method to the analysis of the axisymmetric snap buckling behaviour of uniformly loaded, imperfect, tapered circular plates is briefly described. It is then used to carry out a limited study of the effects of: (1) imperfection magnitude, (2) thickness taper ratio and (3) support conditions on the plate response. Two types of response are distinguished: (a) “snap-through” and (b) “smooth-transition”. The former type of response is found to occur only when the imperfection amplitude is sufficiently large. Furthermore, the results of the study show that decreasing the taper ratio and clamping the plate boundary both serve to raise the snap buckling load and that the latter measure is relatively more efficient in this respect.     

Elasto-plastic buckling of curved webs

This paper presents an investigation on elastic buckling strength of curved girder webs subjected to uniform shears or bending stresses at the edges.An elastic 20 degrees of freedom finite element model was used to formulate the eigenvalue problem and a Gauss-Seidel iterative procedure was employed to yield the lowest critical edge loads.In case of pure bending, the investigation is extended into the plastic range. The deformation theory of plasticity in conjunction with a new formulation of the secant modulus is used to derive the elasto-plastic buckling equations. The same Gauss-Seidel iterative procedure was used to find the critical load for each assumed stress level. Further iterations with incremental stress were done to match the elasto-plastic buckling stresses. The material is assumed to be elastic-perfectly plastic and incompressible.In order to aid design professions, the dimensions of the web panel studied are within the practical ranges of curved plate girders. Four boundary conditions that represent various constrain conditions from flanges to stiffeners of plate girder designs, were considered.The results are presented in graphical forms. Interaction curves relating to various dimensionless parameters are constructed. Comparisons and convergence studies were made with existing available data. It is found that boundary conditions and aspect ratio influence the buckling stresses greatly. However, curvature effect is relatively insignificant over the range of practical application.     

Vibration and buckling analysis of axisymmetric polar orthotropic circular plates

The vibration and stability analysis of polar orthotropic circular plates using the finite element method is discussed. In order to formulate the eigenvalue problems associated with the vibration and stability analyses, the clement stiffness, mass, and stability coefficient matrices are presented. By assuming the static displacement function, which is an exact solution of the polar orthotropic circular plate equation, approximates the vibration and buckling modes, the mass and stability coefficient matrices are readily derived from the given displacement function. Results showing the effects of orthotropy on natural frequencies and buckling loads are compared with their isotropic counterpart.     

Effect of shear deformation on the yielding of circular plates

Shear Deformation Plate Theory (SDPT) is used to analyse the first yield response of axisymmetric circular plates. Expressions for the first yield pressure and the associated plate centre deflection of uniformly loaded, simply supported and clamped plates are presented. Corresponding Classical Thin Plate Theory (CPT) expressions are also deduced. It is demonstrated that the SDPT and CPT expressions are related via correction factors which are functions of the plate thickness-ratio β, and Poisson's ratio. Graphs of the correction factors plotted against β are presented. They illustrate that inherent shear flexibility causes a slight reduction in the first yield pressure compared with the CPT value when the plate edges are simply supported and a slight increase when they are clamped. Plate centre deflections are, however, increased significantly for both support conditions.     

Elasto-plastic finite element analysis of orthotropic rotating discs with holes

The elasto-plastic stress analysis of orthotropic rotating discs with holes has been carried out by the finite element method (FEM). An isoparametric rectangular element with nine nodes has been chosen and the Lagrange polynomial has been used as interpolation function. Steel-aluminium composite has been manufactured by upsetting under the pressure and the temperature. Mechanical properties and yield strengths of composite material have been obtained experimentally by using a strain gauge in the tensile testing machine. The expansions of plastic regions have been illustrated for various cases. Residual stresses and tangential stresses have been shown on the elasto-plastic boundaries of the disc. The limit of angular velocities of the orthotropic disc have been increased by using tangential residual stresses and tangential stresses in the disc subjected to the centrifugal force.     

Numerical and experimental validation of out-of-plane resonance closed formulas for MEMS suspended plates with square holes

A compact analytical model for out-of-plane resonance evaluation is proposed for large diffuse MEMS vibrating plates with squared holes. A closed form expression was developed from a structural reduced order model with equivalent concentrated mass and stiffness parameters. Results were validated through FEM models and experimental modal analysis. Numerical FEM simulations were performed by 1D, 2D and 3D FEM models; experiments on polysilicon test structures were conducted using an interferometric microscope. Specimens were designed ad hoc to highlight the sensitivity of proposed formulas to main structural dimensional parameters of vibrating plates. Experiments and models helped investigate the sensitivity of the proposed reduced linearized model when exposed to electrostatic non-linear coupling effects and fluidic damping coupling. Both numerical results and experiments are in good agreement with analytical results predicted by closed formulas.     

Static,vibration and buckling analysis of axisymmetric circular plates using finite elements

The static, vibration, and buckling analysis of axisymmetric circular plates using the finite element method is discussed. For the static analysis, the stiffness matrix of a typical annular plate element is derived from the given displacement function and the appropriate constitutive relations. By assuming that the static displacement function, which is an exact solution of the circular plate equation ?²?²W = 0, closely represents the vibration and buckling modes, the mass and stability coefficient matrices for an annular element are also constructed. In addition to the annular element, the stiffness, mass, and stability coefficient matrices for a closure element are also included for the analysis of complete circular plates (no center hole). As an extension of the analysis, the exact displacement function for the symmetrical bending of circular plates having polar orthotropy is also given.     

Flexural vibration of shear deformable circular and annular plates on ring supports

This paper presents an analysis of free flexural vibration of circular and annular Mindlin plates lying on multiple internal concentric ring supports. The Rayleigh-Ritz method with an admissible displacement function expressed in terms of a set of simple polynomials is used to obtain the governing eigenvalue equation. The natural frequencies of circular and annular Mindlin plates with one or two ring supports having inner and outer peripheries with different combinations of free, simply supported and clamped conditions are determined. A comprehensive set of vibration results is presented and, where possible, these have been verified with existing solutions published in the open literature. No previous theoretical results for thick annular plates supported with internal rings are known to exist. Thus the study should be useful and valuable to engineers and researchers.     

Elasto-plastic analysis of orthogonally stiffened plates with initial imperfections under uniaxial compression

In general, the stiffened plates consisting of steel plate elements are unavoidably accompanied by initial imperfections such as residual stresses and initial deflections, which have considerable effects on their ultimate strength. Therefore, it is needed for designing them to develop more rational method taking the ultimate strength influenced by initial imperfections into account rather than the conventional design method being on the basis of the linear elastic buckling theory.From this point of view, this study aims to evaluate rigorously the ultimate strength of orthogonally stiffened plate with initial imperfections under uniaxial in-plane compression. The elasto-plastic finite element method is applied to attain this purpose. By a happy combination of modal analytical technique and conventional finite element method, much reduction of the degree of freedom can be expected to be realized herewith. Some numerical calculations are performed by means of this rigorous method to examine the exactness of the analysis. Moreover, the numerical results are compared with the experimental ones.     

Bending of circular plates with variable profile

The technique of Dynamic Relaxation is invoked in analysing the bending of circular plates with variable profile and the results are compared with available exact solutions. The excellent correlation suggests that the technique can serve as an alternative for computing the magnitudes and distributions of moments and deflections in circular plates of anisotropic material with variable profile.     

In-plane and shear buckling analysis of FG-CNTRC annular sector plates based on the third-order shear deformation theory using a numerical approach

The buckling analysis of thick composite annular sector plates reinforced with functionally graded carbon-nanotubes (CNTs) is presented under in-plane and shear loadings based on the higher-order shear deformation theory. It is considered that the plate is resting on the Pasternak-type elastic foundation. The overall material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are estimated through the micromechanical model. The governing equations are derived on the basis of the higher-order shear deformation plate theory, and the quadratic form of the energy functional of the system is presented. An efficient numerical method is presented in the context of variational formulation to obtain the discretized version of stability equations. The validation of the present study is demonstrated through comparisons with the results available in the literature and then comprehensive numerical results are given to investigate the impacts of model parameters on the stability of CNT-reinforced composite annular sector plates.     

Analysis of optimized plates for buckling

This paper is concerned with the analysis of optimized plates for buckling. The Rayleigh-Ritz technique is used to solve variable thickness rectangular plates. A double sine series is used to represent the lateral displacements and convergence is attained for a six term series. The result yields a buckling load which is 44% higher than that of a uniform thickness plate having the same volume. The plate itself was optimized using variational calculus to obtain the optimality condition which states that the thickness is proportional to the strain energy density and a truncated Fourier series solution (one term) was used to obtain an optimal shape having a critical load 112% higher than the uniform thickness plate.     

Axisymmetric substitute structures for circular disks with noncentral holes

For economical finite element calculations of aero-engine disks it is advantageous to use an axisymmetric FE-model. However, disks often contain noncentral holes, for example bolt holes which disturb the axial symmetry. In the present article methods are described on how to find axisymmetric substitute structures for these local disturbances. The substitute structures have been constructed in such a way that the stresses they predict reproduce those in the original structure far away from the hole region. The stresses in the original structure were calculated by applying the formulas obtained by Muskhelishvili for a ring and for a hole in infinite space in an alternating way. An important asset of the substitute structures is that they allow for the prediction of the stress peaks occurring at the hole surfaces. This has been achieved by the determination of appropriate stress concentration factors which must be applied to the respective model stresses. For the practically relevant cases, the developed substitute structures are independent of the specific load conditions and only depend on a single geometric parameter characterizing the relative distance between the holes.     

Finite element buckling analysis of stiffened plates

An isoparametric stiffened plate bending element for the buckling analysis of stiffened plates has been presented. In the present approach, the stiffener can be positioned anywhere within the plate element and need not necessarily be placed on the nodal lines. The element, being isoparametric quadratic, can readily accommodate curved boundaries, laminated materials and transverse shear deformation. The formulation is applicable to thin as well as thick plates. The buckling loads for various rectangular and skew stiffened plates with varying skew angles and stiffness parameters have been indicated. The results show good agreement with those published.     

Seminumerical solution for buckling of rectangular plates

A semianalytical, seminumerical method of solution is presented for the governing partial differential equation of rectangular plates subjected to in-plane loads. The basic functions in the y-direction are chosen as the eigenfunctions for straight prismatic beams. The classical method of separation of variables is employed to obtain an ordinary differential equation. The resulting equation is solved by a one-dimensional finite difference technique. The problem is then reduced to a typical eigenvalue problem which on solution yields the buckling coefficient of the plate. The method is applied on plates with different edge conditions and under various loading conditions. The results are compared with those of existing solutions. Results for the case when one loaded edge is fixed and the other simply supported were reported in the literature for the first time.