Search

The present study develops a new finite element (FE) formulation for the lateral torsional buckling (LTB) analyses of steel beams exteriorly bonded with orthotropic fiber-reinforced polymer (FRP) layers. The formulation considers shear deformations, partial material interaction, local and global warping deformations, and orthotropic FRP properties. The buckling responses of multispan FRP-bonded steel beams predicted by the present solutions are excellently validated against experiment and numerical solutions. As observed, the FRP strengthening is highly effective for the LTB resistance of steel beams. However, the LTB responses are strongly dependent on the orthotropic properties and strengthening lengths of FRP layers. The effects of shear deformations, span ratios, and loading conditions on the LTB responses are also quantified in the present study.

In this study, the influence of concentrated damage on the stability of beams under static loads is investigated according to a co-rotational-based large displacement approach. Well-known benchmark beam-like structures have been considered under different loading conditions and damage scenarios. The concentrated damage has been modelled by means of a cross section reduction of a beam element, following a strategy already adopted in the literature. The results have been expressed in terms of buckling loads and post-buckling responses for different damage scenarios associated with a concentrated damage characterized by different positions, intensities, and extensions.

The analysis of a critical buckling temperature is dependent on the new displacement function field provided in the literature and uses third-order shear deformation theory. The value of the parameter “m,” which determines the new displacement function, closed with the three-dimensional (3D) elasticity results. Thermal critical buckling is analyzed for thick and thin laminated plates by using the Navier solution for symmetric and anti-symmetric cross-ply simply supported boundary conditions. Several design parameters are considered such as extension thermal coefficient ratio (α 1⁄α 2), number of schemes, thickness ratio (a/h), aspect ratio (a/b), and modular ratio (E 1/E 2) when analyzing the dynamic behavior of the critical buckling temperature for different materials, including composite (glass/epoxy) and hybrid (glass/carbon/epoxy), under uniformly distributed temperature load. The accuracy for theoretical results by using Matlab R2019b was checked with other results for different researchers and gave good agreement. Increasing orthotropic ratio and aspect ratio resulted in increasing critical buckling temperature in M1 than M2, whereas increasing thickness ratio, thermal coefficient expansion, and number of layers resulted in decrease in critical buckling temperature in M2 than M1.

In this study, four absolute nodal coordinate formulation (ANCF)-based approaches are utilized in order to predict the buckling load of Lee’s frame under concentrated load. The first approach employs the standard two-dimensional shear deformable ANCF beam element based on the general continuum mechanics (GCM). The second approach adopts the standard ANCF beam element modified by the locking alleviation technique known as the strain-split method. The third approach has the standard ANCF beam element with strain energy modified by the enhanced continuum mechanics formulation. The fourth approach utilizes the higher-order ANCF beam element based on the GCM. Two buckling load estimation methods are used, i.e., by tracing the nonlinear equilibrium path of the load–displacement space using the arc-length method and applying the energy criterion, which requires tracking eigenvalues through the dichotomy scheme. Lee’s frame with different boundary conditions including pinned–pinned, fixed-pinned, pinned-fixed, and fixed–fixed are studied. The complex nonlinear responses in the form of snap-through, snap-back, and looping phenomena during nonlinear postbuckling analysis are simulated. The critical buckling loads and buckling mode shapes obtained through the energy criterion-based buckling method are obtained. After the comparison, higher-order beam element is found to be more accurate, stable, and consistent among the studied approaches.

In this work, an application of two noded beam finite element methodology, which is demonstrated in the previous research work for vibration analysis of beam with a flexible joint problem, has been further extended here to investigate the buckling behaviour of free–free beam subjected to an in-plane compressive load. Joint is modelled as rotational spring, where the rotational spring stiffness governs the behaviour of the flexible joint. Variation of first five non-dimensional buckling loads of free–free beam with reference to the joint location as well as joint stiffness parameters are briefly presented. It is understood that looseness of the joint can significantly influence the buckling behaviour of free–free beam and plays an important role in accurately determining the buckling behaviour of jointed beams subjected to an in-plane compressive loads.

A machine part subjected to an axial compressive load is called strut. But, a vertical strut is known as a column. The machine members that must be investigated for the column action are connecting rods, piston rods, screw jack, etc. When a column is subjected to a compressive load and this load is gradually increased, a stage will be reached when the column will be subjected to ultimate load. Beyond this, the column will fail by crushing, and the load will be known as crushing load. When the column is short or intermediate, sometimes this column fails by bending, i.e. buckling. When the column is long, the value of buckling load is low for long columns and is relatively high for intermediate columns. The present investigation focuses on the testing and evaluation of the mechanical end buckling columns (samples) using 304 stainless steel under dry, corrosion, and combined dry with shot peening (SP) process. The buckling behavior of the axial compressive load has been studied experimentally and theoretically using Euler and Rankin theories. The results obtained from the above study manifested that the column, whose slenderness ratio (SR) is more than 120, is denoted as the long column, and the Euler theory can be successfully used. But, when the SR is less than 120, the column is known as an intermediate one. The mechanical and buckling properties exhibited a reduction due to the corrosion media and a reasonable improvement when using SP.

In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully obtain a general inequality for its eigenvalues. By applying this general inequality, if the complete SMMSs considered satisfy some curvature constraints, we can obtain a universal inequalities for eigenvalues of this buckling problem.

The cylindrical filament wound composite overwrapped pressure vessels (COPV) with metal liner has been widely used in spaceflight due to their high strength and low weight. After the autofrettage process, the plastic deformation of the metal liner is constrained by composite winding layers, which introduce depressions to the metal liner that causes local buckling. To predict the local buckling of the inner liner with depressions of the pressure vessel after the autofrettage process, a local buckling analysis method for the metal liner of COPV was developed in this article. The finite element method is used to calculate the overall stress distribution in the pressure vessel before and after the autofrettage process, and the influence of local depressions on the buckling is evaluated. The axial buckling of the pressure vessel under external pressure is analyzed. The control equation of the metal liner with depressions is developed, considering the changes in the pressure and the bending moment of the liner depressions and its vicinity during the loading and unloading process. Taking the cylindrical COPV (38 L) with aluminum alloy liner as an example, the effects of liner thickness, liner radius, the thickness-to-diameter ratio, autofrettage pressure, and the length of straight section on the autofrettage process are discussed. The results show that the thickness of the inner liner has the most significant influence on the buckling of the liner, followed by the length of the straight section and the radius of the inner liner, while the autofrettage pressure has the least influence.

Due to the need for structures with refined properties to bear against different loading conditions, recently, carbon nanotubes (CNTs) have been used widely to reinforce them. The extremely high stiffness of CNTs makes them significant as one of the best reinforcements to improve the mechanical behaviors of structures. This work focuses on microbeam buckling response with an initial curvature that includes three layers. The mid-layer that is known as the core is constituted of functionally graded porous (FGP) materials and two CNT-reinforced composite skins are bonded to the core to integrate it. The whole structure is affected by the hygrothermal environment and springs and shear layers are put below it. For the first time, for such a structure, a refined shear deformation theory (RSDT) as a higher-order theory that considers thickness stretching effect in polar coordinates is used that presents more accurate results, especially for deeply curved beams. Modified couple stress theory (MCST) in combination with the virtual displacement principle is utilized to establish the governing equations. The obtained results demonstrate the significance of porosity percentage and CNTs’ addition to the skins on the critical nanotubes buckling load. Also, the different behaviors of the microstructure at various temperatures are analyzed and discussed in detail.

This study experimentally investigates the effect of the opening configuration on the buckling stability and bearing performance of a structural beam web used in a commercial aircraft made of composite materials. The buckling and strength analyses on three opening configurations (circular, oblong, and rhombic) were carried out using test samples with identical web surface size. It is found that the rhombic opening has the minimum effect on the buckling stability and strength of the structure. To compensate for the effect of the opening, two reinforcement methods, using reinforcement rib and thickening the sample, were also investigated in this study. It is concluded that thickening the sample can more effectively improve the buckling stability and strength performance of beam web structure and hence has relatively higher structural reinforcement efficiency.

The influence of a wide temperature range in the glass transition region of a shape memory polymer (SMP) matrix on micro-buckling of the fiber reinforcements in shape memory polymer composites (SMPC) under large bending deformation is described. Analytical expressions to estimate the strain energy, neutral strain surface, critical buckling surface and half wavelength of the buckled fibers in the SMPC are presented based on the minimum energy method. This study considers the reinforced fibers as three-dimensional elastic bodies and the matrix as a temperature stimulated flat plate. A comprehensive study was performed to understand the dynamic temperature behavior of the micro-buckled fibers and corresponding results were validated by previous works in the literature. The effects of fiber volume fraction and thickness of the SMPC plates on the half wavelength are also discussed along with the simultaneous influence of temperature on the parameters computed in the minimum energy analysis.

In this study, a thermal buckling analysis of laminate composite square plate was performed with elliptical hole cutout using the finite element method. Graphite/Epoxy laminate plate used in this study is symmetrical stacking sequence plate [(0/90)2]s. This laminate square plate was subjected to temperature loading with clamped support on all edges. Moreover, the parameters considered were fiber orientation (θ), a/b ratio (elliptical hole), elliptical hole inclination (φ), thermal expansion coefficient ratio (α1/α2), and thickness of plates (t). The results showed that as the thermal expansion coefficient ratio changes, the elliptical hole ratio and the elliptical hole inclination have inconsequential effects on the performance of the resistance of laminate composite plates. The maximum values of thermal buckling amplification factor were obtained when the ratio a/b = 1.0, which is a circle cutout,while the minimum values were obtained when the ratio a/b = 0.5, regardless of the thickness of plates. Moreover, the plate with elliptical or circle cutout hole provides about 4% to 9% higher buckling resistance than that of the plate without hole cutout, because when subjected to temperature loading the plate with hole can release stress better than the plate without hole.

The analytical model applicable to calculate the equivalent stiffnesses of composite box beam has been refined. The calculation of equivalent stiffness coefficients of composite laminated box beam is simplified and the connection between shear-deformable beam theory and classical laminate theory is established. The equivalent stiffness analytic formulas expressed by beam cross-section geometry and laminate stiffness coefficients are obtained. These analytical formulas are suitable for composite laminated box beam with circumferential uniform stiffness, and accounts for bending- transverse shear and torsiontensile coupling effect. The correctness and precision of refined analytical model is verified by test and finite element method, respectively. The influences of the lay-ups on the elastic coupling of composite structures and their causes are studied. The variation of the equivalent stiffnesses of the laminated box beams with different lay-ups is predicted. The global buckling analysis of composite laminated box beam considering the transverse shear deformation is carried out. The formula of the global buckling critical load is obtained combining with the theoretical formulas of equivalent stiffnesses. The influences of the lay-ups, shear deformation and slenderness ratio on the global buckling critical load are studied.

This paper presents an experimental investigation of overall buckling behaviour of carbon fibre reinforced plastic (CFRP) tubes with different off-axis ply orientations. A series of specimens are designed and prepared with stacking sequences [0∘4/±θ∘], with θ corresponding to either 0, 90, 45 or 60. Axial compression tests with effective end-reinforcement and hinge support are performed to investigate the overall buckling behaviour. With respect to the future design and application of CFRP tubes with this type of stacking sequence, column curves for each stacking sequences and all test data are fitted based on Perry-Robertson formula. With respect to the high stress level in the relatively short CFRP tube that facilitates the development of defects, test data present high levels of discreetness. We propose a strategy for engineering safe design in which a reduction factor is added to the original reduction factor based on statistical analysis when the universal slenderness ratio is less than 2.

In present paper, buckling analysis is performed over laminated composite beam incorporating multi walled carbon nanotube (MWCNT) polymer matrix and then reinforced with E-glass fiber in an orthotropic manner under inplane varying thermal and mechanical loads by finite element method (FEM). Aim of the study is to develop a model which accurately perform the buckling deterministic analysis of multi-walled carbon nanotube reinforced composite laminated beam (MWCNTRCLB) with the evaluation of material property by applying Halpin–Tsai model. Combined Higher order shear deformation theory and Pasternak elastic foundation based on von Karman nonlinear kinematics and Winkler cubic nonlinearity respectively, are successfully implemented. Through minimum potential energy principle, generalized static analysis is performed using FEM, based on interactive MATLAB coding. The critical buckling load and critical buckling temperature is presented under the action of inplane variable mechanical and thermal load, with different boundary conditions, beam thickness ratio and MWCNT aspect ratio, variation with MWCNT volume fraction and coefficient of thermal expansion, with and without foundation for linear and nonlinear cases.

In the present work, new inverse hyperbolic higher-order shear deformation theory (IHHSDT) is proposed and implemented for buckling analysis and free vibration analysis of porous Functionally Graded Material (FGM) plate on the foundation. The proposed theory follows the approximately parabolic distribution of the transverse stresses through the plate thickness and satisfies the conditions of continuity and differentiability. Three different types of porosity distribution considered. Governing differential equations (GDEs) of the plate is developed in the framework of proposed theories by Hamilton’s principle. Multiquadrics radial basis function (MQ-RBF) based Meshfree method used for discretizing the GDEs. The result obtained by the present theory is validated with the three-dimensional elastic theory and other available solutions in the literature to ensure the efficacy and accuracy of the proposed theory. Numerical results obtained for buckling and free vibration for porous FGM plate resting on the foundation. Effect of grading index, porosity fraction, porosity distribution, the effect of foundation, and the span to thickness ratio have discussed. The secured results can consider as a benchmark for future studies.

In this paper, two computationally efficient techniques viz. Differential Quadrature Method (DQM) and Differential Transformation Method (DTM) have been used for buckling analysis of Euler-Bernoulli nanobeam incorporation with the nonlocal theory of Eringen. Complete procedures of both the methods along with their mathematical formulations are discussed, and MATLAB codes have been developed for both the methods to handle the boundary conditions. Various classical boundary conditions such as SS, CS, and CC have been considered for investigation. A comparative study for the convergence of DQM and DTM approaches are carried out, and the obtained results are also illustrated to demonstrate the effects of the nonlocal parameter, aspect ratio (L/h) and the boundary condition on the critical buckling load parameter.

A three-dimensional (3D) semi-analytical model is developed by introducing meshfree local radial point interpolation method into a Hamilton system to analyze the mechanical and thermal buckling behavior of rectangular laminated plates with embedded delaminations. A modified Hamiltonian function for mechanical and thermal buckling analysis of rectangular laminated composite plates subjected to in-plane axial compressive or thermal loads is proposed. The final governing equation is deduced with the transfer matrix technique and a spring layer model based on the modified Hellinger-Reissner variational principle. One of the main superiorities of the present model is that the scale of final governing equation, which involves only the so-called state variables at the top and bottom surfaces, is insensitive to the thickness and the number of layers of composite laminates. Several relevant numerical examples are carried out to validate the present model, and the present results are in good agreement with pre-existing results.

Buckling tests were conducted using slender specimens of western hemlock. In the tests, the slenderness ratio was varied from 132 to 418 in which elastic buckling was induced, and the values of the critical load for buckling were obtained. When the deflection of the specimen was calculated from the loading-line displacement based on elastica theory, the value of deflection/load initially decreased because the compressive deformation was more dominant than the bending deformation. In contrast, when the load increased, the bending deformation became dominant, and the deflection/load-deflection relation exhibited linearity. These tendencies indicated that the transition from compression to bending was induced around the minimum value of the deflection/load. Therefore, it was recommended to determine the critical load for buckling using the load at the minimum value of the deflection/load where the deflection was calculated from the loading-line displacement. [ABSTRACT FROM AUTHOR]

A genetic algorithm-based method is proposed to globally optimize the stacking sequence of multi-sandwich-panel composite structures for minimum weight with strength and buckling considerations. The prerequisites for the continuity between sandwich panels are first studied. To implement the summarized continuity rules in the evolutionary optimization, three newly constructed chromosomes are developed to encode the global stacking sequence with no additional repair. Genetic operators, including specialized mutation, swapping and crossover operators, are also developed to effectively explore the design space and keep the continuity rules followed. The Hashin criterion and maximum stress criterion are used to evaluate the strength of sandwich panels. A typical multi-sandwich-panel composite structure with identical and different core thicknesses is optimized to verify the validity and efficiency of the proposed method. It is found that much lighter solutions are obtained with an acceptable efficiency in all cases. It is also found that the weight of the multi-sandwich-panel composite structures can be further reduced when the core thicknesses are not identical.

The buckling and layer failure characteristics of composite laminated cylinders subjected to hydrostatic pressure were investigated through finite element analysis for underwater vehicle application. The Tsai-Wu failure criteria were used as the failure criteria for the buckling analysis. A sensitivity analysis was conducted to research the influence of the number of elements on the critical buckling pressure. ANSYS, a finite element program, successfully predicted the buckling pressure with 5.3–27.8% (linear) and 0.3–22.5% (nonlinear) deviation from experimental results. The analysis results showed that the cylinders can carry more pressure after a slight decrease in pressure and recovery of the supporting load. For layer failure analysis, it was found that the failure that occurred in the 0° layer was more serious than that in the 90° layer within the neighboring layers at the inner layers (nos. 1–7) and outer layers (nos. 8–24).

Fiber reinforced anisotropic material abounds in biological world. It has been demonstrated in previous theoretical and experimental works that growth of biological soft tubular tissue plays a significant role in morphogenesis and pathology. Here we investigate growth-induced buckling of anisotropic cylindrical tissue, focusing on the effects of type of growth(constraint/unconstraint, isotropic/anisotropic), fiber property(orientation, density and strength), geometry and any interaction between these factors. We studied one-layer and two-layer models and obtained a rich spectrum of results. For one-layer model, we demonstrate that circumferential fiber orientation has a consistent stabilizing effect under various scenarios of growth. Higher fiber density has a destabilizing effect by disabling high-mode buckling. For two-layer model, we found that critical buckling strain at inner boundary is an invariant under same isotropic growth rate ratio between inner/ outer layer(g1 /g0). Then we applied our model to wound healing and illustrate the effects of skin residual stress, fiber property, proliferation region width and wound size on the wound edge stability. We conclude that fiber-reinforcement is an important factor to consider when investigating growth induced instability of anisotropic soft tissue.

In the present work, the small size effects on stability properties of perforated microbeams under various types of deformable boundary conditions are studied considering the Fourier sine series solution procedure and a mathematical procedure known as Stokes' transformation for the first time. The main benefit of the present method is that, in addition to considering both the gradient elasticity and the size effects, the kinematic boundary conditions are modeled by two elastic springs as deformable boundary conditions. The deformable boundary conditions and corresponding stability equation are described using the classical principle which are then used to construct a linear system of equations. Afterward, an eigenvalue problem is adopted to obtain critical buckling loads. The correctness and accuracy of the present model are demonstrated by comparing results with those available from other works in the literature. Moreover, a numerical problem is solved and presented in detail to show the influences of the perforation properties, geometrical, and the variation of small-scale parameters and foundation parameters on the stability behavior of the microbeams. In addition, according to the best knowledge of the authors, there is no study in the literature that examines the buckling behavior of perforated microbeams on elastic foundation with the gradient elasticity theory. [ABSTRACT FROM AUTHOR]

Recently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

In this paper, thermal buckling analysis of composite laminated beams resting on a two-parameter elastic foundation is carried out by means of the variational iteration method (VIM). The solution procedure is based on the first-order shear deformation beam theory of Timoshenko combined with the von Karman type of geometrical non-linearity. Both edges of the beam are assumed to be axially restrained while may possess various out-of-plane boundary conditions. The elastic foundation is modelled via the two-parameter Pasternak medium which takes into account the vertical interaction of the elements. The governing equilibrium equations are obtained by means of the virtual displacement principle. Stability equations are then obtained by means of the adjacent equilibrium criterion. These equations are uncoupled to extract individual equations in terms of lateral displacement. The resulted differential equations are solved via the VIM. The study examines the VIM in obtaining the closed-form analytical solutions for thermal buckling of composite laminated beams. Furthermore, it is shown that for some special materials with negative thermal expansion coefficient, buckling may occur under cooling rather than heating or it may not occur at all.

Experimental studies were made on isotropic cylindrical panels made of Aluminum 7075-T6 under uniaxial compression. The experimental values of the critical buckling load were determined using four different methods. The critical buckling load was also determined using MSC/NASTRAN and CQUAD8 finite element. The experimental values of the critical buckling load obtained by different methods were compared with the finite element solution. The effects of the panel angle, panel length and panel thickness on the critical buckling load of isotropic cylindrical panels made of Aluminum 7075-T6 were studied. It is found that the Method III (based on a plot of applied load versus average axial strain) yields the highest value for critical buckling load and Method II (based on a plot of applied load versus square of out-of-planede deflection) the lowest value for critical buckling load. The experimental values given by Method III are seen to be closest to the finite element solution. Critical buckling load increases monotonically as panel angle increases.

Experimental studies were made on isotropic skew plates made of aluminum 7075-T6 and laminated composite skew plates under uniaxial compression with unloaded edges completely free and one loaded edge restrained completely and the other loaded edge restrained except translationally in the direction of loading. Experimental values of the buckling load have been determined using five different methods. The buckling load has also been determined using CQUAD8 finite element of MSC/NASTRAN. Comparison is made between the various experimental values of buckling load and the finite element solution. The effects of the skew angle and the aspect ratio on the critical buckling load of isotropic skew plates made of aluminum 7075-T6 have been studied. The effects of the skew angle, aspect ratio, and the laminate stacking sequence on the critical buckling load of laminated composite skew plates have also been studied. The critical buckling load is found to increase with the increase in the skew angle and decrease with the increase in aspect ratio. Method IV yields the highest value for critical buckling load and Method III the lowest value for critical buckling load. Among the various experimental values, the one given by Method IV is closest to the finite element solution, and the discrepancy between them is less than about 5% in the case of isotropic skew plates and about 10–15% in the case of laminated composite skew plates.

The fiber steering capability of automated fiber placement machines offers the designers more room to fully exploit the directional properties of composite materials. Circumferential stiffness tailoring by fiber steering can considerably increase the bending-induced buckling performance of laminated composite cylinders. The potential structural improvement resulting from fiber steering depends on different design parameters such as the number of plies considered for fiber steering in a laminate. In this study, the buckling performance improvement of a variable stiffness (VS) composite cylinder is investigated for different percentages of plies considered for fiber steering in a multilayered composite laminate. A surrogate-based modeling along with a multi-step optimization is used in the design procedure of this study. The improvements in the buckling performance are shown and verified using finite element analysis in ABAQUS software. The mechanisms leading to buckling performance improvement of VS composites are also investigated and presented for different percentages of fiber-steered plies.

The present paper presents the finite element studies made on critical buckling load of isotropic and laminated composite cylindrical skew panels. Analysis is performed using CQUAD4 and CQUAD8 elements of MSC/NASTRAN. It is found that the CQUAD8 element yields better results compared to the CQUAD4 element in terms of accuracy and convergence. Using the CQUAD8 element, the effects of the panel angle, skew angle, aspect ratio, and length-to-thickness ratio on the critical buckling load of isotropic cylindrical skew panels have been studied. The effects of additional parameters such as fiber orientation angle, numbers of layers (NL), and stacking sequence on the critical buckling load of laminated composite cylindrical skew panels have also been studied. The critical buckling loads are found to increase with the increase in panel angle and skew angle. When the NL in the laminate is large, the variation of the critical buckling load with the NL is not appreciable. The boundary conditions are found to have significant influence on the critical buckling load.

The aim of this experimental study is to investigate the buckling behaviors after impact of the composite plates. The increasing impact energies, which ranged from approximately 3–15 J, are performed at three different impact points of the composite plates having three different thicknesses until vicinity of the penetration threshold of specimens. After the impact tests, the effects of the different impact points, energy levels, and thickness on the buckling behaviors of the impacted specimens are investigated. Also, compared with nonimpacted specimens, the buckling loads are presented nondimensionally. As expected, the lowest critical buckling load occurs in thin plates impacted at the center point. The critical buckling loads become more stable both by increasing number of layers and in the impact points that are away from the center.

In this paper, the buckling load optimisation is performed on sandwich cylindrical panels. A finite element program is developed in MATLAB to solve the governing differential equations of the global buckling of the structure. In order to find the optimal solution, the genetic algorithm Toolbox in MATLAB is implemented. Verifications are made for both the buckling finite element code and also the results from the genetic algorithm by comparisons to the results available in literature. Sandwich cylindrical panels are optimised for the buckling strength with isotropic or orthotropic cores with different boundary conditions. Results are presented in terms of stacking sequence of fibers in the face sheets and core to face sheet thickness ratio.

Cutouts such as circular, rectangular, square, elliptical, and triangular shapes are generally used in composite plates as access ports for mechanical and electrical systems, for damage inspection, to serve as doors and windows, and sometimes to reduce the overall weight of the structure. This paper addresses the effects of different cutouts on the buckling behavior of plates made of polymer matrix composites. To study the effects of cutouts on buckling, loaded edges are taken as fixed and unloaded edges are taken as free. Finite element analysis is also performed to predict the effects of different geometrical cutouts, orientations, and position of cutouts on the buckling behavior. The results show that fiber orientation angle and cutout sizes are the most important parameters on the buckling loads. For all types of cutouts the buckling loads decrease dramatically by increasing the fiber orientation angle. It is observed that minimum buckling load is reached when 45° fiber angle is used, and after this angle critical buckling load begins to increase. Also, it is concluded that while fiber orientation angle is 0°, elliptical cutout has the highest buckling load and while fiber orientation angle is 45°, circular cutout has the highest buckling load.

In this study, thermal buckling load optimization of symmetrically laminated composite folded plates subjected to uniformly distributed temperature load is investigated. The objective function is to maximize the critical temperature capacity of laminates and the fiber orientation is considered as a design variable. The first-order shear deformation theory is used to study thermal buckling response of the laminates. The modified feasible direction method is used as the optimization routine. For this purpose, a program based on Fortran is used for the optimization. Finally, the significant effects of crank angles, plate lengths and boundary conditions on the optimum results are demonstrated and the results are compared.

In this article, Carrera’s Unified Formulation (CUF) is combined with a radial basis function collocation technique. A higher-order theory that considers deformations in the thickness direction was developed under CUF to predict the buckling behaviour of laminated plates. The obtained governing equations and boundary conditions are then interpolated by collocation with radial basis functions. The accuracy and efficiency of the combination of the two techniques for buckling problems of laminated plates are demonstrated through numerical experiments.

For curves of prescribed length embedded into the unit disk in two dimensions, we obtain scaling results for the minimal elastic energy as the length just exceeds 2π and in the large length limit. In the small excess length case, we prove convergence to a fourth-order obstacle-type problem with integral constraint on the real line which we then solve. From the solution, we obtain the energy expansion 2π + Θδ1/3 + o(δ1/3) when a curve has length 2π + δ and determine first order coefficient Θ ≈ 37. We present an application of the scaling result to buckling in two-layer cylindrical shells where we can determine an explicit bifurcation point between compression and buckling in terms of universal constants and material parameters scaling with the thickness of the inner shell. [ABSTRACT FROM AUTHOR]