Biaxial Compressive Loads Research Articles

Damage characteristics and constitutive modeling of the 2D C/SiC composite: Part II – Material model and numerical implementation

In this work, a macroscopic non-linear constitutive model accounting for damage, inelastic strain and unilateral behavior is proposed for the 2D plain-woven C/SiC composite. A set of scalar damage variables and a new thermodynamic potential expression are introduced in the framework of continuum damage mechanics. In the deduced constitutive equations, the material’s progressive damage deactivation behavior during the compression loading is described by a continuous function, and different deactivation rates under uniaxial and biaxial compression loadings are also considered. In damage evolution laws, the coupling effect among the damage modes and impediment effect of compression stress on the development of shear damage in different plane stress states are taken into account. Besides, the general plasticity theory is applied to describing the evolution of inelastic strain in tension and/or shear stress state. The Tsai–Wu failure criterion is adopted for strength analysis. Additionally, the material model is implemented as a user-defined material subroutine (UMAT) and linked to the ABAQUS finite element software, and its performance is demonstrated through several numerical examples.

Mechanical behaviour of different types of concrete under multiaxial compression

The strength of concrete under biaxial compression and triaxial compression is higher than the strength under uniaxial compression, but the level of increase is affected by factors such as the type of concrete, differences in testing machines, loading rate, etc. Based on this, an experimental investigation into the strength of normal air-entrained concrete (NAEC) under biaxial and triaxial compression loading conditions was carried out. The experimental results on NAEC were compared with the multiaxial compression strengths of other types of concrete obtained using the same testing machine. According to the test data, failure criteria and multiaxial ultimate strength envelopes in principal stress space were proposed. The test results indicated that biaxial compressive strength is higher than uniaxial compressive strength and the maximum increase of ultimate strength occurred at a biaxial compression stress ratio of 0·5 for all types of concrete. A relationship between biaxial compressive strength, triaxial compressive strength and stress ratio was developed. This work provides theoretical and experimental foundations for strength analysis of concrete structures.

Behavior of pyramidal lattice core sandwich CFRP composites under biaxial compression loading

Pyramidal lattice core sandwich composites all made of CFRP is believed to have superior characteristics, as compared to the conventional composite and sandwich plates. Several articles addressed the behavior of this type of composite in the literature. However, its response under biaxial compression loading and its notch sensitivity was not covered within the current state-of-the art.In the current paper, numerical simulation tools were used to examen the failure mechanisms and the notch sensitivity of the pyramidal lattice core sandwich CFRP composite. The simulations adopted the LaRC failure criteria and property degradation rules. The model took into account the fiber tension and compression, the matrix tension and compression and the fiber matrix shear out failure mechanisms. The problem was solved with and without holes in order to examen the notch sensitivity. The model was validated against experimental results from the literature and showed good agreement. The results showed that these types of structures are less sensitive to notches, as compared to the traditional composites, which may guarantee the use of these structures in bolted joint and similar applications.

Stability of carbon nanotube-reinforced composite plates with surface-bonded piezoelectric layers and under bi-axial compression

Based on Reissner’s mixed variational theorem (RMVT), we develop a unified formulation of finite layer methods (FLMs) for the three-dimensional (3D) buckling analysis of simply-supported, functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plates with surface-bonded piezoelectric actuator and sensor layers and under bi-axial compressive loads. In this work, a set of membrane stresses is assumed to exist just before instability occurs, and determined using the predefined 3D deformations for the prebuckling state. The carbon nanotubes (CNTs) are considered to be uniformly distributed (UD), and FG rhombus- and X-type variations through the thickness coordinate, and the effective material properties of the FG CNTRC layer are evaluated using the rule of mixtures, and two different surface conditions, open- and closed-circuit, are considered. In the formulation, the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations for the field variables of each individual layer, respectively. The accuracy and convergence of the FLMs with various orders used for the expansion of each field variable in the thickness are assessed by comparing their solutions with the exact 3D ones available in the literature.

3D buckling analysis of FGM sandwich plates under bi-axial compressive loads

Based on the Reissner mixed variational theorem (RMVT), finite rectangular layer methods (FRLMs) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, fiber-reinforced composite material (FRCM) and functionally graded material (FGM) sandwich plates subjected to bi-axial compressive loads. In this work, the material properties of the FGM layers are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively, and an h-refinement process is adopted to yield the convergent solutions. The accuracy and convergence of the RMVT-based FRLMs with various orders used for expansions of each field variables through the thickness are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.

Buckling Analysis of Rectangular Functionally Graded Material Plates under Uniaxial and Biaxial Compression Load

Abstract This article deals with the buckling analysis of rectangular functionally graded material (FGM) plates using classical plate theory (CPT). Finite element method has been applied for the modelling and buckling analysis of FGM plate. Uniaxial and biaxial compression loads along with simply supported boundary conditions on rectangular FGM plates are investigated. Convergence of the solution obtained by MATLAB has also been studied by varying the mesh size. Obtained results are compared with the existing literature, it shows that the buckling characteristics are closer to the reference results. By varying the geometric parameter a/b critical buckling load variation has been calculated and Power law index is also been evaluated.

Strain-induced martensitic transformation in stainless steels: A three-dimensional phase-field study

A three-dimensional elastoplastic phase-field model is developed to study the microstructure evolution during strain-induced martensitic transformation in stainless steels under different stress states. The model also incorporates linear isotropic strain hardening. The input simulation data is acquired from different sources, such as CALPHAD, ab initio calculations and experimental measurements. The results indicate that certain stress states, namely uniaxial tensile, biaxial compressive and shear strain loadings, lead to single variant formation in the entire grain, whereas others, such as uniaxial compressive, biaxial tensile and triaxial strain loadings, lead to multivariant microstructure formation. The effects of stress states, strain rate as well as temperature on the mechanical behavior of steels are also studied. The material exhibits different yield stresses and hardening behavior under different stress states. The equivalent stress is higher at low strain rate, whereas a higher elongation is obtained at high strain rate. The deformation temperature mainly affects the hardening behavior of the material as well as the transformation, i.e. martensite volume fraction decreases with increasing temperature. Some of the typical characteristics of strain-induced martensite, such as the formation of thin elongated martensite laths, shear band formation and nucleation of martensite in highly plasticized areas, as well as at shear band intersections, are also observed.

Biaxial wrinkling analysis of composite-faced sandwich plates with soft core using improved high-order theory

Abstract In the present paper, an improved high-order theory is used for wrinkling analysis of sandwich plates with soft orthotropic core. Third-order plate theory is used for the facesheets and quadratic and cubic functions are assumed for transverse and in-plane displacements of the core, respectively. Continuity conditions for transverse shear stresses at the interfaces as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of the plate are satisfied. The nonlinear Von-Karman type relations are used to obtain strains. Also, the transverse flexibility and transverse normal strain and stress of the orthotropic core are considered. The equations of motion and boundary conditions are derived by principle of minimum potential energy. Analytical solution for static analysis of simply supported sandwich plates under biaxial in-plane compressive loads is presented using Navier's solution. The effect of geometrical parameters of the facesheets and the core and the biaxial loads ratio are studied on the buckling and wrinkling behavior of sandwich plates. Comparison of the present results with the published results in the literature for the special case, confirms the accuracy of the proposed theory. Results showed that the increase in the biaxial load ratio, cause to change the direction of wrinkling wave propagation.

Analysis of failure modes of latticed sandwich skins under biaxial compression load

The failure modes of open weave (latticed) sandwich skins under biaxial compression load are analysed. Due to the latticed structure of these sandwich face sheets, they are able to transfer loads in both directions. Tests show a distinct non-linear correlation between load and deformation. This non-linear load-deflection-behavior indicates that the failure may be induced by geometrical imperfections. Based on this assumption and measured geometrical imperfections, a mathematical model for the latticed face sheet consisting of beams under compression is derived. Several beams are combined within one or two cells of the honeycomb core to describe the failure modes. Furthermore, biaxial loading is analysed by using the finite element method. Experimental results are in good agreement with failure loads derived by analytical and by finite element method analyses as well.

A full compatible three-dimensional elasticity element for buckling analysis of FGM rectangular plates subjected to various combinations of biaxial normal and shear loads

In the present paper, a three-dimensional elasticity approach is employed to investigate buckling of heterogeneous functionally graded plates under biaxial compression, shear, tension-compression, and shear-compression load conditions. In this regard, a formulation that employs a full compatible three-dimensional Hermitian element with 168 degrees of freedom and guarantees continuity of the strain and stress components is used. It is known that all of the available famous commercial finite element softwares and the proposed series solutions satisfy continuity conditions of the displacement rather than the stress components. Buckling occurrence is detected based on checking both the instability onset and equilibrium criteria. Results are extracted based on a Galerkin-type orthogonality. Therefore, they are more accurate than those obtained based on the traditional Ritz method. The presented three-dimensional finite element analysis and the extracted results are quite new. A vast variety of results including results of biaxial compression, compression-tension, shear, and shear-compression load cases is considered and discussed in detail.

Postbuckling response of composite laminated plates with evolving damage

In this paper, postbuckling behavior and progressive failure of laminated plates considering geometric nonlinearity and evolving material damage under uniaxial, biaxial compressive and in-plane shear loadings are studied. The damage model is based on a generalized macroscopic continuum theory within the framework of irreversible thermodynamics and enables to predict the progressive damage and failure load. Damage variables are introduced for the phenomenological treatment of degradation of the stiffness properties of laminated plates due to microscopic defects. The analysis is carried out using field-consistent finite element approach based on first-order shear deformation theory. The nonlinear governing equations are solved using the Newton–Raphson iterative technique coupled with the adaptive displacement control method to trace the pre- and postbuckling equilibrium path. The damage evolution equations are solved at every Gauss point using Newton–Raphson iterative technique within each loading/displacement increment iteration. The detailed parametric study is carried out to investigate the influences of evolving damage, span-to-thickness ratio, lamination scheme, boundary conditions and aspect ratio on the postbuckling response and failure load of laminated plates under in-plane loading. The ratio of failure load to buckling load increases with increase in thickness ratio due to the dominating restoring action of in-plane stretching forces in postbuckling region of thin plates whereas the thick plates depict material failure prior to buckling point. Thin plates with SSFF boundary conditions with evolving damage depict softening postbuckling response whereas the plates with other boundary conditions considered depict hardening response.

Buckling and vibration of rectangular plates of variable thickness with different end conditions by finite difference technique

This paper is concerned with the determination of exact buckling loads and vibration frequencies of variable thickness isotropic plates using well known finite difference technique. The plates are subjected to uni, biaxial compression and shear loadings and various combinations of boundary conditions are considered. The buckling load is found out as the in plane load that makes the determinant of the stiffness matrix equal to zero and the natural frequencies are found out by carrying out eigenvalue analysis of stiffness and mass matrices. New and exact results are given for many cases and the results are in close agreement with the published results. In this paper, like finite element method, finite difference method is applied in a very simple manner and the application of boundary conditions is also automatic.

Two-pheromone Ant Colony Optimization to design dispersed laminates for aeronautical structural applications

The objective of the present study is to find out the effect of using non-conventional fiber orientations (orientations not limited to 0^o, +/-45^o and 90^o) to improve the composite material response. The Ant Colony Algorithm is used to optimize the stacking sequence for biaxial tension and compression loading condition under strength constraints. Moreover, a modified algorithm (two-pheromone algorithm) is used to design a fully dispersed laminate. Results show that dispersed laminates can improve the critical buckling load by up to 8% for the biaxial compression loading case. With respect to the biaxial tensile loading condition, the results show that the matrix cracking failure index can be decreased up to 100% and the fiber tensile failure index can be decreased by 40% using the two pheromone formulation.

Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method

This paper addresses the elastic buckling and vibration characteristics of isotropic and orthotropic nanoplates using finite strip method. In order to consider small scale effect, Eringen’s nonlocal continuum elasticity is employed. The governing nanoplate equations are derived using the principle of virtual work while B3-spline finite strip method is applied to the buckling and vibration analyses. The buckling load and vibration frequency of graphene sheets, which are subjected to biaxial compression and pure shear loading, are determined whilst the effects of different parameters such as sheet size, nonlocal parameter, aspect ratio and boundary conditions are investigated. The interaction curves of the critical biaxial compression loading as well as the interaction curves of the critical uniaxial compression and shear loading are also obtained. It is shown that small scale effect plays considerable role in the analysis of small sizes plates.

Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion

In this paper, the buckling problem of thin rectangular functionally graded plates subjected to proportional biaxial compressive loadings with arbitrary edge supports is investigated. Classical plate theory (CPT) based on the physical neutral plane is applied to derive the stability equations. Mechanical properties of the FGM plate are assumed to vary continuously along its thickness according to a power law function. The displacement function is considered to be in the form of a double Fourier series whose derivatives are determined using Stokes' transformation. The advantage of this method is capability of considering any possible combination of boundary conditions with no necessity to be satisfied in the Fourier series. To give generality to the problem, the plate is assumed to be elastically restrained by means of rotational and translational springs at the four edges. Numerical examples are presented, and the effects of the plate aspect ratio, the FGM power index, and the loading proportionality factor on the buckling load of an FGM plate with different usual boundary conditions are studied. The present results are compared with those have been previously reported by other analytical and numerical methods, and very good agreement is seen between the findings indicating validity and accuracy of the proposed approach in the buckling analysis of FGM plates.

Buckling analysis of stiffened plates subjected to non-uniform biaxial compressive loads using conventional and super finite elements

This paper presents the buckling analysis of stiffened plates, using both conventional and super finite element methods. Mindlin plate and Timoshenko beam theories are utilized so as to formulate the plate and stiffeners, respectively. The arbitrary oriented stiffeners can be positioned anywhere within the plate element and are not limited to be placed on nodal lines. Therefore, any configuration of plate and stiffeners can be modeled. Furthermore, extensive boundary conditions as well as general in-plane loading conditions can be considered using the proposed method. As the applied in-plane loads are not uniform, the buckling load is evaluated in two steps. First, the elasticity problem is solved to determine the stress distribution in prebuckling stage. Applying the principle of minimum potential energy, based on derived stress distribution, yields to the buckling equation of stiffened plates. Numerical examples are proposed to study the accuracy and efficiency of the developed super elements. Effects of various combinations of biaxial loads along with different boundary conditions on buckling characteristics of stiffened panels are also investigated.

Post-Buckling Stability Analysis of Composite Laminated Flat Plates with Initial Deflection under Biaxial Compression

Advanced fiber-reinforced laminated plates have been used as structural members in various applications by virtue of their high specific strength and stiffness. This paper considers, by use of the second variation of the total potential energy, secondary buckling of cross-ply laminated plates with an initial deflection under biaxial compression that is simply supported along four edges. The occurrence of secondary buckling is proven analytically and the effects of the initial deflection, outer lamination angle, number of layers, biaxial compressive load ratio and post-buckling deflection pattern are discussed. [doi:10.2320/matertrans.M2013111]

Estimation of Ultimate Limit Statefor Stiffened-Plates Structures: Applying for a Very Large Ore Carrier Structures Designed by IACS Common Structural Rules

In advanced marine industry, the reduction in weight of hull structures for a very large object ship plays an important role as the economic efficiency is the most significant aspect. In this paper, we investigate the ultimate strength of structural ship stiffened-plates designed by International Association of Classification Societies (IACS) Common Structural Rules (CSR) methods of collapse state, by applying for ANSYS nonlinear finite element analysis (FEA). Specifically, the ultimate limit assessment methods for the outer bottom of ship structures, which have drawn a significant attention from industrial marine and offshore structures, are proposed to reduce the weight of ship structures. To solve this, we study the structures of a hypothetical Very Large Ore Carrier (VLOC) designed by pre-CSR and CSR methods. In particular, the stiffened-plates under the biaxial compression and lateral pressure loads with simply supported or/and clamped boundary condition(s), the results ultimate limit state assessment performance of Nonlinear FEA methods are shown and compared to various states.

Optimum Stacking Sequence Design of Composite Sandwich Panel Using Genetic Algorithms

In the present study, both critical buckling load maximization and face-sheet laminate thickness minimization problems for the composite sandwich panel, subjected to bi-axial compressive loading under various imposed constraints have been investigated using genetic algorithms. In the previously published work, the optimization of simple composite laminate panels with only even number of laminae has been considered [1, 3]. The present work allows the optimization of a composite sandwich panel with both even and odd number of laminae in the face-sheet laminates. Also, the effects of the bending-twisting coupling terms (D16 and D26) in bending stiffness matrix which were neglected in the previous studies [1, 2, 3], are considered in the present work for exact solutions. In addition effect of both balanced and unbalanced face-sheet laminates on the optimum solutions have also been investigated, whereas only balanced laminates were considered in the previous studies [1, 2, 3].

Thermal post-buckling analysis of square plates resting on elastic foundation: A simple closed-form solutions

Thermal post-buckling paths of homogeneous, isotropic, square plate configurations resting on elastic foundation (Winkler type) subjected to biaxial compressive thermal loads are expressed as simple closed-form solutions by using the Rayleigh–Ritz method based on coupled displacement fields. Geometric non-linearity of von-Karman type is considered. The in-plane displacement field variations used in the formulation of Rayleigh–Ritz method are derived by using the governing in-plane static differential equations of the plate which in turn simplifies the difficulty of assuming an in-plane displacement field variations of the square plate. Accuracy and robustness of the proposed closed-form solutions are demonstrated by using the non-linear finite element formulation results which are obtained from an equilibrium path approach.