In engineering practice, it is difficult to guarantee that the foundation of a beam is homogeneous along the whole length. This paper presents an investigation on buckling and post-buckling behavior ...of beams on the elastic foundation under thermal loading. The virtual work method is employed to deduce the buckling governing equation and post-buckling differential equation of equilibrium. The Buckling load of beams on homogeneous foundation is investigated analytically and it is found that the first buckling mode is determined by nondimensional foundation stiffness. The beam will jump to another mode at a certain value of foundation stiffness. This paper investigates the buckling and post-buckling behavior of beams on elastic foundation under thermal loading. The buckling and post-buckling behaviors of beams on weakened foundation are analyzed by using a shooting technique. The results show that the weakening effect has a significant influence on buckling temperature and buckling mode, and post-buckling path is stable in the whole loading process under thermal effects. It is also observed that the weakening effect can give rise to local deformation of the beam, and the location of the weakening effect has an obvious influence on buckling mode and post-buckling deformation.
Cutouts are always located in aerospace composite structures to meet specified requirements on the service and functions. The presence of cutout, especially large-sized cutout, would result in a ...significant stress concentration, and consequently a complicated failure mechanism. This paper presents an experimental and numerical study on the post-buckling damage process of high-performance carbon fiber reinforced polymer (CFRP), T800/X850, multidirectional composite laminated specimen. The simply supported specimen is with a central large-sized elliptical cutout and subjected to shearing load. In the numerical analysis, a damage model incorporating both advanced strain softening schemes and cross-coupling effect between the failure mechanisms is constructed for the damage simulation. Regularizations are implemented for coupling the damage variables to address the deficiencies of the existing model and access the real physical damage behavior of laminated composites. The strain invariant failure theory is employed for evaluation of delamination. To assess the objectivity of the present numerical model, the numerical predictions are compared with experimental data. The predicted damage and propagation patterns show good agreement with experiment results.
A post-buckling model of cylindrical shells with local thickness defects is established based on the Hamiltonian system. The homotopy analysis method and the symplectic eigensolution expansion method ...are combined to obtain the post-buckling equilibrium path and post-buckling modes of the cylindrical shells with defects. By constructing an eigenvalue buckling problem of the defective cylindrical shell as a zero-order homotopy deformation equation, a significantly better convergence rate can be obtained when compared to the classical perturbation method. The result shows that the defects can induce unique local dents and significantly reduce the ultimate post-buckling bearing capacity of the cylindrical shells. The research finds important and practical applications in many engineering fields that use cylindrical shells as key design components, in particular in aerospace and aeronautical engineering, marine engineering, automobiles, civil engineering, etc.
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●A post-buckling model of cylindrical shell with thickness defects is established.●Homotopic analysis and eigensolution expansion method are combined to obtain the buckling modes.●Thickness defect causes post-buckling equilibrium path to become steady.●Rectangular thickness defect is more unfavorable to buckling than cruciform.
Abstract
Even though the simulations used to describe the failure of laminates are becoming more and more predictive, complex testing under multiaxial loadings is still required to validate the ...design of structural parts in a wide range of industrial domains. It is thus essential to assess the actual boundary conditions to allow for an objective comparison between testing and calculations, in particular since the structural tests are complex and often leads to buckling. Therefore, accurate estimation of force and moment fluxes applied to the specimen is critical. In this context, stereo digital image correlation (SDIC) has proven to be an important measurement tool and provides very well‐resolved surface displacement fields, but the exploitation of such measurements to calculate fluxes remains problematic when testing composites. The first objective of this study is both to reduce the uncertainty associated with fluxes determination on a complex test and to simplify the extraction process with respect to existing procedures. The second objective is to make this methodology robust to geometrically non‐linear deformations. In this paper, we propose a new methodology that extracts minimal boundary conditions in the form of 3D mechanically admissible displacements fields. The approach developed uses a finite element SDIC (FE‐SDIC) method regularized by means of mechanical behaviour admissibility equations. Results show that the new methodology outputs much more accurate fluxes than classical data generated from multiple differentiations of the displacement fields. Excellent noise robustness is obtained and quantified. Numerical predictions have been satisfactorily compared with experimental data from one structural‐scale composite specimen under complex testing.
The article presents results of experimental investigations of thin-walled beams made with carbon fiber composite. Experimental studies were conducted to confirm results obtained from numerical ...calculations, which was performed using two different software based on finite element method and analytical–numerical method based on Koiter’s asymptotic stability theory of conservative systems modified by Byskov and Hutchinson. The studies consisted of axially compressed thin-walled columns with channel and top-hat cross section.
The specimen for the tests were made of unidirectional composite – epoxy resin matrix with carbon fibers reinforcement. The specimen was manufactured using autoclave technique. Thin-walled channel columns with dimensions of 80×40×1.048mm and length of 300mm and with four different symmetrical ply arrangements were prepared.
The resulting axial force, longitudinal shortening and lateral displacement were recorded during experimental tests. Additionally in chosen points the strain were registered using strain gauges measurement technique.
The experimental critical loads using the different method were determined. The experimental results was compared with these obtained from finite element method (ANSYS and ABAQUS) and analytical–numerical method. The postbuckling equilibrium paths obtained from experimental tests and numerical calculation for all considered columns were compared.
A full scale experimental investigation into the strength and behaviour of prestressed steel stayed columns in compression has been conducted. Results, including full load versus end-shortening ...curves, for a total of 18 test specimens are presented. Two critical modes of buckling — symmetric and antisymmetric — with interactive post-buckling are demonstrated experimentally and the imperfection sensitivity of the stayed columns is investigated. Interactive buckling is observed primarily when the individual buckling loads of the antisymmetric and symmetric modes are close or when the antisymmetric mode is critical. Analysis of the results reveals that increased prestress leads to an increased load-carrying capacity when instability occurs in the symmetric mode, but the reverse trend is found when the antisymmetric mode is critical.
► Full-scale experimental investigation of prestressed steel stayed columns. ► Physical demonstration of antisymmetric and interactive buckling for the first time. ► Antisymmetric mode tends to trigger interactive post-buckling. ► Increasing prestress found to increase capacity in symmetric mode. ► Increasing prestress found to decrease capacity in antisymmetric mode.
Thermal post-buckling and nonlinear vibration behaviors of FGM beams are analyzed by using concept of physical neutral surface, von Kármán strain-displacement relationships and high order shear ...deformation theory. Material properties are assumed to be temperature dependent and vary along the thickness. The prominent character of physical neutral surface higher-order shear deformation beam theory is that stretching-bending couplings are eliminated in constitutive equations, and governing equations have the similar forms as homogeneous isotropic beams. Approximate solutions are given out by Ritz method, and influences played by different supported boundaries, thermal environmental conditions and volume fraction index are discussed in detail.
Wrinkling phenomena of stiff thin films on compliant substrates are investigated based on a non-linear finite element model. The resulting non-linear equations are then solved by the Asymptotic ...Numerical Method (ANM) that gives interactive access to semi-analytical equilibrium branches, which offers considerable advantage of reliability compared with classical iterative algorithms. Bifurcation points are detected through computing bifurcation indicators well adapted to the ANM. The effect of boundary conditions and material properties of the substrate on the bifurcation portrait is carefully studied. The evolution of wrinkling patterns and post-bifurcation modes including period-doubling has been observed beyond the onset of the primary sinusoidal wrinkling mode in the post-buckling range.
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•A classical film/substrate model is analysed by advanced numerical methods.•Dimensional analysis of the model is performed.•Generic bifurcation schemes are established.•The effect of boundary conditions and material properties is investigated.•Bifurcation points on non-linear response curves and post-buckling modes including period-doubling are captured.
The Koiter–Newton method has been proved to be a computationally efficient method for buckling and post-buckling analysis of structures, using a novel reduced-order modeling strategy. In this paper, ...the existing method is extended for laminated composite plates with delamination. We develop a 4-node quadrilateral element S4DE as a geometric linear element in the co-rotational formulation of the Koiter–Newton method. The assumed layerwise displacement model of the developed element is enriched with Heaviside unit step functions to model delamination. The displacement fields of each layer are described using the superposition of first-order shear deformation and layerwise functions. The zig–zag theory is applied to enhance the numerical accuracy and computational efficiency of the developed element. The construction of the reduced order model requires derivatives of the strain energy with respect to the degrees of freedom up to the fourth order, which is two orders more than traditionally needed for a Newton based nonlinear finite element technique. The geometrical nonlinearities are taken into account using derivatives of the local co-rotational frame with respect to global degrees of freedom. Various laminated plates with different thicknesses, delamination lengths and stacking sequences are considered to validate the good performance of the present method in terms of numerical reliability, accuracy and computational effort.
This paper presents a three-dimensional beam element for stability analysis of elastic thin-walled open-section beams in multibody systems. The beam model is based on the generalized strain beam ...formulation. In this formulation, a set of independent deformation modes is defined which are related to dual stress resultants in a co-rotational frame. The deformation modes are characterized by generalized strains or deformations, expressed as analytical functions of the nodal coordinates referred to the global coordinate system. A nonlinear theory of non-uniform torsion of open-section beams is adopted for the derivation of the elastic and geometric stiffness matrices. Both torsional-related warping and Wagner’s stiffening torques are taken into account. Second order approximations for the axial elongation and bending curvatures are included by additional second order terms in the expressions for the deformations. The model allows to study the buckling and post-buckling behaviour of asymmetric thin-walled beams with open cross-section that can undergo moderately large twist rotations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. Some validation examples illustrate the accuracy and computational efficiency of the new beam element in the analysis of the buckling and post-buckling behaviour of thin-walled beams under various loads and (quasi)static boundary conditions. Finally, applications to multibody problems are presented, including the stability analysis of an elementary two-flexure cross-hinge mechanism.
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