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In this paper, the recently-developed floating node method is extended for damage analysis of laminated composites with large deformations. Strong discontinuities including interfacial delamination and matrix cracks are explicitly represented by geometrically nonlinear kinematics. Interactions between these two kinds of failure patterns are enabled through enriched elements equipped with floating nodes. A cohesive zone model is utilized for the damage process zone. A general implicit procedure with user-defined elements is developed for both quasi-static and dynamic analysis. The performance of this formulation is verified with two benchmark simulations, involving buckling-induced delamination and low-velocity impact damage. The results presented show good quantitative and qualitative agreements with results from literature. [ABSTRACT FROM AUTHOR]

We present a computational method that can be applied to capture surface stress and surface tension-driven effects in both stiff, crystalline nanostructures, like size-dependent mechanical properties, and soft solids, like elastocapillary effects. We show that the method is equivalent to the classical Young-Laplace model. The method is based on converting surface tension and surface elasticity on a zero-thickness surface to an initial stress and corresponding elastic properties on a finite thickness shell, where the consideration of geometric nonlinearity enables capturing the out-of-plane component of the surface tension that results for curved surfaces through evaluation of the surface stress in the deformed configuration. In doing so, we are able to use commercially available finite element technology, and thus do not require consideration and implementation of the classical Young-Laplace equation. Several examples are presented to demonstrate the capability of the methodology for modeling surface stress in both soft solids and crystalline nanostructures. [ABSTRACT FROM AUTHOR]

The paper is concerned with eigen buckling analysis of curvilinear shells with and without cutouts by an effective meshfree method. In particular, shallow shell, cylinder and perforated cylinder buckling problems are considered. A Galerkin meshfree reproducing kernel (RK) approach is then developed. The present meshfree curvilinear shell model is based on Reissner-Mindlin plate formulation, which allows the transverse shear deformation of the curved shells. There are five degrees of freedom per node (i.e., three displacements and two rotations). In this setting, the meshfree interpolation functions are derived from the RK. A singular kernel is introduced to impose the essential boundary conditions because of the RK shape functions, which do not automatically possess the Kronecker delta property. The stiffness matrix is derived using the stabilized conforming nodal integration technique. A convected coordinate system is introduced into the formulation to deal with the curvilinear surface. More importantly, the RKs taken here are used not only for the interpolation of the curved geometry, but also for the approximation of field variables. Several numerical examples with shallow shells and full cylinder models are considered, and the critical buckling loads and their buckling mode shapes are calculated by the meshfree eigenvalue analysis and examined. To show the accuracy and performance of the developed meshfree method, the computed critical buckling loads and mode shapes are compared with reference solutions based on boundary domain element, finite element and analytical methods. [ABSTRACT FROM AUTHOR]

Compressive tests involving buckling are known to be defect sensitive, nevertheless, to our knowledge, no inverse approach has been proposed yet to use this property for the localization and characterization of material defects. This is due to geometric imperfections, which greatly influence and even dominate the response of defective parts under compression. In comparison with a system lacking geometric imperfections, the modified system does not present any bifurcation, showing that the non-linear progressive response is mainly governed by such imperfections. Before implementing any inverse procedures it is necessary to know whether extracting meaningful material defect information from compressive tests on specimen which also have geometric imperfections is possible. To tackle this issue, an equivalent eigenvalue problem will be extracted from the non-linear response, a problem corrected from geometric imperfections. A dedicated inverse formulation based on the modified constitutive relation error will then be constructed which will involve only well-posed linear problems. Examples illustrate the potential of the methodology to localize and identify single and multiple defects. [ABSTRACT FROM AUTHOR]

Second order buckling theory involves a one-way coupled coupled problem where the stress tensor from a plane stress problem appears in an eigenvalue problem for the fourth order Kirchhoff plate. In this paper we present an a posteriori error estimate for the critical buckling load and mode corresponding to the smallest eigenvalue and associated eigenvector. A particular feature of the analysis is that we take the effect of approximate computation of the stress tensor and also provide an error indicator for the plane stress problem. The Kirchhoff plate is discretized using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces. The same finite element spaces can be used to solve the plane stress problem. [ABSTRACT FROM AUTHOR]

A computational method is proposed for the analysis and prediction of instability (wrinkling or necking) of multilayered compressible plates and sheets made by metals or polymers under plane strain conditions. In previous works, a basic assumption (or a physical argument) that has been frequently made is that materials are incompressible to simplify mathematical derivations. To account for the compressibility of metals and polymers (the lower Poisson's ratio leads to the more compressible material), we propose a combined semi-numerical algorithm and finite element method for instability analysis. Our proposed algorithm is herein verified by comparing its predictions with published results in literature for thin films with polymer/metal substrates and for polymer/metal systems. The new combined method is then used to predict the effects of compressibility on instability behaviors. Results suggest potential utility for compressibility in the design of multilayered structures. [ABSTRACT FROM AUTHOR]

Thin-walled members that have one dimension relatively large in comparison to the cross-sectional dimensions are usually modelled by using beam-type one-dimensional finite elements. Beam-type elements, however, are based on the assumption of rigid cross-section, thus they only allow considerations associated with the beam axis behaviour such as flexural-, torsional- or lateral-buckling and cannot consider the effects of local deformations such as flange local buckling or distortional buckling. In order to capture the local effects of this type shell-type finite element models can be used. Based on the Bridging multi-scale approach, this study proposes a numerical technique that is able to split the global analysis, which is performed by using simple beam-type elements, from the local analysis which is based on more sophisticated shell-type elements. As a result, the proposed multi-scale method allows the usage of shell elements in a local region to incorporate the local deformation effects on the overall behaviour of thin-walled members without necessitating a shell-type model for the whole member. Comparisons with full shell-type analysis are provided in order to illustrate the efficiency of the method developed herein. [ABSTRACT FROM AUTHOR]

A mixed atomistic and continuum model is applied to carbon nanotubes, in order to study their buckling behavior. Herein, the term 'atomistic' refers to the underlying constitutive model that is formulated on the basis of interatomic potentials, whereas 'continuum' means the application of the Cauchy-Born rule, which links the bond vectors before and after deformation via the deformation gradient of the continuum. Because the bond vectors are not infinitesimal and the continuum is modeled as surface, the Cauchy-Born rule has to be appropriately adapted to crystalline sheets. This is done via an exponential mapping in a new and surprisingly simple form such that in the analysis the current configuration has never to be left. The numerical buckling analysis of carbon nanotubes using the mixed atomistic and continuum model is carried out by means of the finite element method. For this purpose, the linearization of the equilibrium equations is provided. [ABSTRACT FROM AUTHOR]

This paper presents a numerical algorithm based on a perturbation technique named asymptotic numerical method (ANM) to solve nonlinear problems with hyperelastic constitutive behaviors. The main advantages of this technique compared to Newton-Raphson are: (a) a large reduction of the number of tangent matrix decompositions; (b) in presence of instabilities or limit points no special treatment such as arc-length algorithms is necessary. The ANM uses high order series approximation with auto-adaptive step length and without need of any iteration. Introduction of this expansion into the set of nonlinear equations results into a sequence of linear problems with the same linear operator. The present work aims at providing algorithms for applying the ANM to the special case of compressible and incompressible hyperelastic materials. The efficiency and accuracy of the method are examined by comparing this algorithm with Newton-Raphson method for problems involving hyperelastic structures with large strains and instabilities. [ABSTRACT FROM AUTHOR]

The paper deals with the perturbation energy concept and its application to stability of imperfection sensitive structures under time-dependent loads. The evaluation of the stability is based on energy norms, which may be used for investigation of safety against buckling. Starting from a stable state of equilibrium the presented procedure allows to decide whether the structure stays for a certain load history within critical bounds, which separate the motion round the prebuckling state from a motion in the postbuckling region. The stability is proved by comparing the critical energy calculated by a static analysis and the load induced energy. Applications to a truss and a spherical shell illustrate the variety of the phenomena in dynamic buckling behaviour of elastic structures in case of impulsive loading and the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

From the point-of-view of economy and safety it is desirable to employ structural configurations with a favorable strength-to-weight ratio and a sufficiently small imperfection-sensitivity. The presentation focuses on two examples falling into this category: The axially compressed cylindrical shell filled with – and/or surrounded by - a compliant core, and auxetic structures. Both exhibit unexpected aspects in their load-carrying behavior and have a significant weight-savings potential. [ABSTRACT FROM AUTHOR]

In this paper a numerical modelling of non linear problems involving large deformations and frictional contact conditions is proposed. The motivation of this work comes from the study of the cellular materials (such as wood or foams) undergoing strong deformations. We restrict our study to a regular cellular network of hexagonal cells with thin walls. Strong loadings can generate at first buckling phenomena, then self-contact in the cell. Renouncing homogenization procedures, not always pertinent in this case, we have developed direct simulations. After giving the mechanical and mathematical formulations of the problem, we present two advanced numerical tools to solve large non linear frictional multicontact problems. This numerical modelling is based on an arc-length continuation method which permits to snap through singular points due to buckling phenomena and on an optimal domain decomposition method adapted to frictional contact problems. Finally, mechanical investigations of the contactless buckling and the post-buckling provide some pertinent parameters controlling the deformation process. [ABSTRACT FROM AUTHOR]

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy’s third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu–Hill equations from which the boundary points on the unstable regions are determined by Bolotin’s method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies. [ABSTRACT FROM AUTHOR]

This paper is concerned with the development of a global p-element method for the analysis of self-weight buckling of thin cylindrical shells. Such buckling problems occur when cylindrical shells are subject to high-g acceleration, for instance the launching of rockets and missiles under high propulsive power. The cylindrical shells may have any combination of free, simply supported and clamped ends. A p-element computational method has been developed based on various thin shell theories including Donnell, Sanders and Goldenveizer-Novozhilov models. The strain energy for the global element during buckling is formulated and an eigenvalue equation is derived. Unlike the conventional buckling problem where the eigenvalue is directly solved, a pre-determined buckling parameter is fixed at the outset for a geometric-dependent stiffness and a recursive numerical procedure is developed to compute the effect of critical buckling length. The critical buckling length is found to be proportional to thickness to a power of approximately 0.9. The effects of shell thickness and length on buckling parameter are also investigated. Comparison of results from various shell theories indicates solutions of the Sanders and Goldenveizer-Novozhilov shell theories are in excellent agreement while the Donnel shell theory is good for buckling of short cylindrical shells. [ABSTRACT FROM AUTHOR]