Biaxial Buckling Research Articles

Influence of Transverse Normal Strain on Buckling and Vibration of Sandwich Plates

This study presents the buckling and free vibration behavior of simply supported square and rectangular sandwich plates. A third-order shear deformation theory considering both the transverse shear and normal deformations is used. The condition of zero transverse shear stresses on the top and bottom surfaces of the plate is satisfied. Hence, the present theory does not require the shear correction factor generally associated with the first-order shear deformation theory. Governing equations and boundary conditions are obtained using the principle of minimum potential energy. The closed-form solutions of simply supported sandwich plates are obtained. The effect of the side-to-thickness ratio and plate aspect ratio on buckling and free vibration responses of simply supported square and rectangular sandwich plates is examined. Parametric effects of face sheet thickness ratios and load factor upon the critical buckling load for uniaxial and biaxial buckling analysis of square and rectangular sandwich plates for different staking sequences are studied. All numerical solutions are obtained using MATLAB® programs. The results obtained from the present theory are compared with those from classical plate theory, first-order shear deformation theory, higher-order shear deformation theories, and the exact three-dimensional elasticity solutions as applicable.

Elastic Buckling of Composite Laminated Plates: A Numerical Investigation

Abstract: This paper presents a numerical method using ANSYS to estimate the buckling loads of composite plates. Our approach employs an element based on FSDT that considers out-of-plane shear deformation. We used an Eight node SHELL281 element that is well-suited for analyzing plate and shell structures. The ANSYS results for buckling loads of isotropic and orthotropic layered laminates are in good agreement with other theories from the literature. In this study, we investigated uniaxial and biaxial buckling of the plates and also considered the degree of orthotropy to study its impact on the plates' buckling.

Computational Model Verification and Validation of Elastoplastic Buckling Due to Combined Loads of Thin Plates

Thin plates are widely used in various engineering applications. In some cases, these structural components may buckle due to compressive loads, which can be aggravated by lateral loads. Several authors have studied the elastoplastic buckling behavior of thin plates considering parameters such as material and geometric properties, support conditions, and initial out-of-plane imperfections. Some studies have also investigated the effects of notches and holes on the ultimate buckling stress of thin plates. The main goal of the present work is to verify and validate a computational model developed using the Finite Element Method via ANSYS® software, to simulate the mechanical behavior of metallic plates under uniaxial or biaxial compression combined with lateral load. The proposed numerical model was verified and validated by comparing its results with analytical, numerical, and experimental solutions found in the literature, reaching maximum differences and errors of around 5%. In sequence, the verified and validated computational model was used in a simple case study: a simply supported plate with a centered rectangular perforation and subjected to an in-plane compressive biaxial load combined with a lateral load, considering five different metallic materials: AISI 4130 steel, AH-36 steel, spheroidal graphite iron (SGI), compact graphite iron (CGI) and Al 7075-T651 aluminum alloy. The results obtained are consistent and, as expected, prove the applicability of the proposed computational model. From this, the biaxial elastoplastic buckling behavior was evaluated, indicating that among the studied cases the higher ultimate stress and the smallest maximum deflection were achieved, respectively, by the plates made of AISI 4130 steel and AH-36 steel.

Recognition of 3D Chiral Microenvironments for Myoblast Differentiation.

Cell chirality plays a critical role in the linkage between molecular chirality and the asymmetrical biological functions of body organs. However, enantioselective interactions between cell chirality and the extracellular environment are not yet fully understood. In this study, we investigated the effects of structurally chiral extracellular microenvironments on cellular alignments and differentiations. Twisted wrinkle-shaped chiral micropatterns were prepared using biaxial and asymmetric buckling methods, wherein structural handedness was determined from the orientation of the tilt angle between the first and second microwrinkles. Myoblasts were separately cultured on two enantiomeric chiral micropatterns in a mirror-reflected shape. Cells cultured on the left-handed chiral micropatterns preferred alignments along the direction of the second microwrinkle, with a relatively deeper valley than that of the first microwrinkle. The aligned cells on the left-handed pattern showed higher differentiation rates, as assessed by fusion indices and marker protein expression levels, than those cultured on right-handed chiral micropatterns. These results suggest that myoblasts exhibit enantioselective recognition of structurally chiral microenvironments, which can promote cellular alignments and differentiation.

Biaxial buckling analysis of an innovative active sandwich plate

Fragility and the presence of a poisonous substance (lead) are the two major issues with traditional piezoceramics and structures that include them. This work suggests an active structure that is lightweight, flexible, and eco-friendly such that a polymeric foam plate is sandwiched between two piezoelectrically activated nanocomposite layers. A combination of a polymer and piezoelectric nanowires (NWs) of zinc oxide (ZnO) is used in the nanocomposite layers. For the proposed active structure, two types of void distributions and functionally graded (FG) distributions of the NWs have been assumed in each corresponding layer. The buckling characterization of the proposed eco-friendly active sandwich plate (EFASP) under biaxial mechanical loads has been conducted using an extended meshless solution based on a third-order theory. An in-depth parametric study on the EFASPs’ biaxial buckling resistance revealed that increasing NW content considerably enhances buckling resistance, with this enhancement strongly reliant on the distribution profile of the NWs. Moreover, it was observed that embedding voids in the substrate layer can lead to a large structural weight reduction while only marginally lowering the buckling performance of suggested EFASPs.

Numerical simulation and constructal design applied to biaxial elastic buckling of plates of composite material used in naval structures

Thin plates when subjected to compressive loads can present a structural instability phenomenon known as buckling, causing displacements out of the plane of the plate. In addition, it is known that the use of composite materials in naval engineering can bring many benefits in the medium and long term, like the major corrosion resistance, when compared with steel structures. Moreover, for specific applications perforated plates are necessary, like passage of cables and pipes, inspection windows, among others. Therefore, to find the optimal geometry of a composite plate with a centered elliptical hole the Constructal Design (CD) was applied in association with the Exhaustive Search (ES) technique and Finite Element Method (FEM). The CD allows the evaluation of the geometry that provides the optimal distribution of imperfections, leading to the maximum value of the performance parameter used for the analysis of solids mechanics problems. Applying different laminations, it was observed an increase in the critical buckling load for a composite plate without perforations of up to 10.47%. In its turn, despite suffering a reduction in the critical load value if compared to the plate without holes, an improvement of 16.89% was observed when optimal and worst geometries for the perforated plates are compared.

Controlled Bi-Axial Buckling and Postbuckling of Thin Films Suspended on a Stretchable Substrate with Square Prism Relief Structures

Stretchable electronics have spurred rapid developments from curvilinear devices to bio-integrated diagnostic and therapeutic devices. The wavy configuration in the device components on a stretchable elastomeric substrate surface plays a prominent role in simultaneously achieving high areal coverage and stretchability without compromising the electric performance, resulting in unique applications in stretchable and flexible light-emitting diodes (LEDs), batteries, supercapacitors, and photovoltaics. In this study, we investigate the buckling behaviors of stiff thin films on the top surface of a biaxially pre-strained elastomeric substrate with square prism micro-patterned structures. Based on energy minimization, a theoretical model is established to study the buckling profiles and the maximum strain for different pre-strain levels along two directions, which agrees reasonably well with those obtained by the finite element analysis (FEA). After revealing the effect of the center-to-center distance in micro-patterned structures and the interfacial contact width between the film and substrate on the buckling behavior, the elastic stretchability of the system is studied.

Verification of Finite Element Computational Model for Biaxial Buckling of Stiffened Plates

This study presents the verification of computational models for the analysis of biaxial buckling in plates. The verification was performed by comparing the numerical results obtained in this study with results found in scientific references published by other authors. The computational models were developed in the ANSYS® software, which is based on the Finite Element Method (FEM), and the SHELL 281 element is used. The mesh convergence tests demonstrate the convergent behavior of the simulations performed for the analyzed examples, which are: a square plate under biaxial elastic buckling, and a rectangular plate with stiffeners under biaxial elasto-plastic buckling. From the converged mesh, maximum differences of 0.84% and 3.89% were achieved when compared with references, respectively, for the elastic and elasto-plastic biaxial buckling. These results indicate that the proposed computational models were adequately verified.

Applicability Evidence of Constructal Design in Structural Engineering: Case Study of Biaxial Elasto-Plastic Buckling of Square Steel Plates with Elliptical Cutout

The application of the Constructal Design method in Heat Transfer and Fluid Mechanics areas is an already consecrated approach to geometrically evaluate these flow engineering systems. However, this approach in Mechanics of Materials realm is not yet widely used, since one can find only few publications about it in literature. The Constructal Design is based on the Constructal Law, a physical law that explains the universal phenomenon of evolution of any finite size flow system. Therefore, the main goal here is to show that the Constructal Design can also be used in dedicated Structural Engineering problems as an effective method for geometric evaluation. The obtained results prove the Constructal Design applicability definitively in Mechanics of Materials.

Numerical analysis of biaxial elasto-plastic buckling of perforated rectangular steel plates applying the Constructal Design method

Thin plates are constantly used in many applications of the structural designs, like naval, aerospace, civil and offshore platforms. When the supported loading is compressive along the plane of plate, it can suffer with an instability phenomenon called buckling which can be elastic or elasto-plastic. In addition, many times the plated structures need to be designed with cutouts for the most varied reasons: access, maintenance, crossing pipes and reducing of weight, for example. The presence of holes affects the mechanical behavior of the plate and it must be investigated. This work used Finite Element Method associated to Constructal Design method and Exhaustive Search technique to find the optimal geometries, i.e. the ones that maximize the Normalized Ultimate Stress, for simply-supported rectangular steel plates under biaxial compressive loading. It was analyzed the size and geometry of the centered elliptical hole. It was observed that the presence of cutout reduces the mechanical strength of the plate and also, the same occurs when the hole size is increased. Constructal Design method has been proved as an effective method to analyze buckling problems conducting to the best geometry for each studied case. For the simulated cases it is evident the relevance of geometric evaluation of elliptical perforations, once the simply variation of geometry can provide differences until around 42% when comparing the optimum and the worst geometries, for the same hole size.

Thermal vibration and buckling analysis of functionally graded carbon nanotube reinforced composite quadrilateral plate

This paper investigates the thermal vibration and buckling of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) quadrilateral plate using the meshless method. Four distributions of the reinforcements along the thickness direction are considered, which are the uniform distributions (UD), FG-V, FG-O and FG-X. The corresponding effective material properties including Young's modulus, mass density, Poisson's ratio and thermal expansion coefficients are estimated by the rule of mixture with the CNT efficiency parameters accounting for the size-dependence. The first-order shear deformation theory (FSDT) with the consideration of thermal effects is employed. Based on Hamilton's principle and the moving least square (MLS) approximation, the discrete governing equations for the vibration of the FG-CNTRC plate are derived. The free vibration of the regular and irregular plates with and without the temperature effect are considered respectively, and the corresponding natural frequencies and mode shapes are obtained by the eigenvalue problem. The stability analysis of the uniaxial and biaxial mechanical and thermal buckling are also conducted subsequently. The effects of the volume fraction, distribution pattern, geometrical characteristics and temperature on the buckling behaviors of the CNTRC quadrilateral plate are discussed in detail.

B EFFECT OF BOUNDARY CONDITIONS ON BUCKLING LOAD FOR LAMINATED COMPOSITE DECKS PLATES

Finite element (FE) method is presented for the analysis of thin rectangular laminatedcomposite decks plates under the biaxial action of in – plane compressive loading. Theanalysis uses the classical laminated plate theory (CLPT) which does not account for sheardeformations. In this theory it is assumed that the laminate is in a state of plane stress, theindividual lamina is linearly elastic, and there is perfect bonding between layers. The classicallaminated plate theory (CLPT), which is an extension of the classical plate theory (CPT)assumes that normal to the mid – surface before deformation remains straight and normal tothe mid – surface after deformation. Therefore, this theory is only adequate for bucklinganalysis of thin laminates. A Fortran program has been developed. New numerical results aregenerated for in – plane compressive biaxial buckling which serve to quantify the effect ofboundary conditions on buckling loading. It is observed that, for all cases the buckling loadincreases with the mode number but at different rates depending on whether the plate is simplysupported, clamped or clamped – simply supported. The buckling load is a minimum whenthe plate is simply supported and a maximum when the plate is clamped. Because of therigidity of clamped boundary condition, the buckling load is higher than in simply supportedboundary condition. It is also observed that as the mode number increases, the plate needsadditional supp

Optimization of Laminated Composite Plates for Maximum Biaxial Buckling Load

This paper proposes an optimization procedure for maximization of the biaxial buckling load of laminated composite plates using the gradient-based interior-point optimization algorithm. The fiber orientation angle and the thickness of each lamina are considered as continuous design variables of the problem. The effect of the number of layers, fiber orientation angles, thickness and length to thickness ratios on the buckling load of the laminated composite plates under biaxial compression is investigated. The effectiveness of the optimization procedure in this study is compared with previous works.

Bi-axial and shear buckling of laminated composite rhombic hypar shells

The bi-axial and shear buckling behavior of laminated hypar shells having rhombic planforms are studied for various boundary conditions using the present mathematical model. In the present mathematical model, the variation of transverse shear stresses is represented by a second-order function across the thickness and the cross curvature effect in hypar shells is also included via strain relations. The transverse shear stresses free condition at the shell top and bottom surfaces are also satisfied. In this mathematical model having a realistic second-order distribution of transverse shear strains across the thickness of the shell requires unknown parameters only at the reference plane. For generality in the present analysis, nine nodes curved isoparametric element is used. So far, there exists no solution for the bi-axial and shear buckling problem of laminated composite rhombic (skew) hypar shells. As no result is available for the present problem, the present model is compared with suitable published results (experimental, FEM, analytical and 3D elasticity) and then it is extended to analyze bi-axial and shear buckling of laminated composite rhombic hypar shells. A C0 finite element (FE) coding in FORTRAN is developed to generate many new results for different boundary conditions, skew angles, lamination schemes, etc. It is seen that the dimensionless buckling load of rhombic hypar increases with an increase in c/a ratio (curvature). Between symmetric and anti-symmetric laminations, the symmetric laminates have a relatively higher value of dimensionless buckling load. The dimensionless buckling load of the hypar shell increases with an increase in skew angle.

Buckling of carbon nanotube (CNT)-reinforced composite skew plates by the discrete singular convolution method

A geometric transformation method based on discrete singular convolution (DSC) is firstly applied to solve the buckling problem of a functionally graded carbon nanotube (FG-CNT)-reinforced composite skew plate. The straight-sided quadrilateral plate geometry is mapped into a square domain in the computational space using a four-node DSC transformation method. Hence, the related governing equations of plate buckling and boundary conditions of the problem are transformed from the physical domain into a square computational domain by using the geometric transformation-based singular convolution. The discretization process is achieved via the DSC method together with numerical differential and two different regularized kernels such as regularized Shannon’s delta and Lagrange-delta sequence kernels. The accuracy of the present DSC results is first verified, and then, a detailed parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of the skew plate and skew angle on the axial and biaxial buckling responses of FG-CNTR composite skew plates with different boundary conditions. Some new results related to critical buckling of an FG-CNT-reinforced composite skew plate are also presented, which can serve as benchmark solutions for future investigations.

Buckling of non-uniformly distributed graphene and fibre reinforced multiscale angle-ply laminates

Present work investigates the biaxial buckling of three-phase, angle-ply laminates reinforced with graphene platelets and carbon or glass fibres. The analysis is based on Classical Plate Theory with the shear effect neglected. The laminate is defined as a three-ply symmetric laminate with simply supported boundary conditions and with different graphene and fibre contents in the surface and middle layers. As such, the laminate has a non-uniform distribution of the reinforcements in the surface and middle layers. Thicknesses of surface and middle layers are also non-uniform, but symmetrical. The objective is to investigate the effect of having a higher content of graphene and fibre in the surface layers as compared to the middle layer and also the effect of the relative thicknesses of the surface and middle layers on the buckling load. The main idea is to produce a cost effective design by concentrating the reinforcements in the surface layers where they are most effective. Thickness of the surface layers can be specified as the minimum required for a given buckling load to reduce the cost and to keep the volume content of the expensive reinforcements to a minimum. Effective properties of the three-phase composite are determined via micromechanical relations. Cost-effective designs using the minimum amount of reinforcements for a given buckling load can be determined from the graphs in the numerical results section. It is observed that relative graphene and fibre contents and thickness ratios of surface and middle layers affect the buckling load at different degrees. It is also observed that higher fibre contents can lead to lower buckling loads if the graphene content exceeds a critical value.

Effect of reversing lamination scheme

New numerical results are generated for in-plane compressive biaxial buckling which serves to quantify the effect of reversing lamination scheme on buckling loading. The buckling loads have been determined for two modulus ratios 40 and 5. It is observed that the buckling loads are completely the same for the given first three modes. Therefore, it can be concluded that the buckling load of laminated plates will remain the same even if the lamination order is reversed. The reason behind this is that the transformed elastic coefficients are equal for both lamination schemes.

Bi-Axial Buckling of Laminated Composite Plates Including Cutout and Additional Mass.

In the presented paper, a study of bi-axial buckling of the laminated composite plate with mass variation through the cutout and additional mass is carried out using the improved shear deformation theory (ISDT). The ISDT mathematical model employs a cubic variation of thickness co-ordinates in the displacement field. A realistic parabolic distribution of transverse shear strains through the plate thickness is assumed and the use of shear correction factor is avoided. A C° finite element formulation of the mathematical model is developed to analyze the buckling behavior of laminated composite plate with cutout and additional mass. As no results based on ISDT for the considered problem of bi-axial buckling of the laminated composite plate with mass variation are available in the literature, the obtained results are validated with the data available for a laminated composite plate without cutout and additional mass. Novel results are obtained by varying geometry, boundary conditions and ply orientations.

Controlled Fabrication of 3D Chiral Microwrinkles via Asymmetrical and Biaxial Bucklings

AbstractNano‐ and microsized chiral materials are receiving significant attention because of their unique characteristics, which include chiroptical activities and enantioselective interactions with living materials. However, the realization of chiral morphologies in such small‐scale materials has been an issue because of the complicated fabrication methods and limited material selection. In this study, a facile and reproducible method is developed for fabricating 3D chiral microwrinkles with twisted shapes by asymmetric and biaxial buckling. Soft polydimethylsiloxane (PDMS) substrates are asymmetrically stretched with angled biaxial strains and exposed to UV/ozone to prepare hard silica layers on top of the PDMS substrates to induce microwrinkles. The chiral shapes are controlled by changing the angle (θ) between the two strain axes and the UV/ozone exposure times (t1, t2) in each stage of buckling. The 3D chiral microwrinkles are shaped like “fusilli pasta” and occupy an area of 1.5 cm × 1.5 cm. The patterned area can be easily scaled, and no innate chiral biomaterial is necessary. This method could be widely extended to the fabrication of diverse types of chiral materials for advanced optical and bio‐applications.

Effect of material anisotropy on buckling load for laminated composite decks plates

New numerical results are generated for in-plane compressive biaxial buckling which serves to quantify the effect of material anisotropy on buckling loading. The coupling effect on buckling loads is more pronounced with the increasing degree of anisotropy. It is observed that the variation of buckling load becomes almost constant for higher values of elastic modulus ratio.