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In this paper, the dynamics and the buckling loads for an Euler–Bernoulli beam resting on an inhomogeneous elastic, Winkler foundation are studied. An analytical, asymptotic method is proposed to determine the stability of the Euler–Bernoulli beam for various types of inhomogeneities in the elastic foundation taking into account different types of damping models. Based on the Rayleigh variation principle, beam buckling loads are computed for cases of harmonically perturbed types of inhomogeneities in the elastic foundation, for cases of point inhomogeneities in the form of concentrated springs in the elastic foundation, and for cases with rectangular inclusions in the elastic foundation. The investigation of the beam dynamics shows the possibility of internal resonances for particular values of the beam rigidity and longitudinal force. Such types of resonances, which are usually typical for nonlinear systems, are only possible for the beam due to its inhomogeneous foundation. The occurrence of so-called added mass effects near buckling instabilities under the influence of damping have been found. The analytical expressions for this “added mass” effect have been obtained for different damping models including space hysteresis types. This effect arises as a result of an interaction between the main mode, which is close to instability, and all the other stable modes of vibration.

A modified total potential energy functional is derived for stress-driven non-local model of Timoshenko beam subject to transverse load and/or critical axial load. The modified functional includes expressions representing the constitutive boundary conditions, which are a peculiarity of the adopted stress-driven approach. The Euler equations of the modified functional are the governing equations of the stress-driven non-local model. Instead of solving directly the Euler equations, approximate solutions are searched by imposing the stationary condition of the modified functional through the Ritz method. In order to validate the method, the proposed numerical solutions are compared with closed-form expressions, in load cases where closed-form solutions are available. Finally, the proposed numerical method is used for determining the buckling load of non-local Timoshenko beam.

The problem of a compressed Timoshenko beam of finite length in frictionless and bilateral contact with an elastic half-plane is investigated here. The problem formulation leads to an integro-differential equation which can be transformed into an algebraic system by expanding the rotation of the beam cross sections in series of Chebyshev polynomials. An eigenvalue problem is then obtained, whose solution provides the buckling loads of the beam and, in turn, the corresponding buckling mode shapes. Beams with sharp or smooth edges are considered in detail, founding relevant differences. In particular, it is shown that beams with smooth edges cannot exhibit a rigid-body buckling mode. A limit value of the soil compliance is found for beam with sharp edges, below which an analytic buckling load formula is provided without loss of reliability. Finally, in agreement with the Galin solution for the rigid flat punch on a half-plane, a simple relation between the half-plane elastic modulus and the Winkler soil constant is found. Thus, a straightforward formula predicting the buckling loads of stiff beams resting on compliant substrates is proposed.

In this paper, the free vibration of axially-loaded, multi-cracked Timoshenko beams with differing boundary conditions, namely, hinged-hinged, fixed-fixed, fixed-hinged, and fixed-free is studied. The cracked beam system is represented as several beam segments connected by massless rotational springs with sectional flexibility. Each segment is assumed to obey the Timoshenko beam theory. A simple transfer matrix method is used to derive the characteristic equation of the axially-loaded, multi-cracked beam with differing boundary conditions. The characteristic equation and corresponding mode shapes are a function of natural frequency, crack size and location, and physical parameters of the beam. In this paper, the effects of crack depth, number of cracks, position of cracks, axial load, shear deformation and rotary inertia on the dynamic behavior of multi-cracked beams are studied in detail. It is found that there is good agreement between the results obtained in this study and results available in the literature. Additionally, interesting observations overlooked by other researchers are obtained.

The purpose of this research is computational morphogenesis while using reduced stiffness method for purpose of increasing the buckling load and decreasing its imperfection sensitivity of latticed shells with free curved surface, consideration of loading imperfection. I perform computational morphogenesis using this technique and grasp the characteristic and tendency of a structure form which are acquired.

In this paper, a new hybrid approach is presented based on the combination of the power series expansions and the Rayleigh-Ritz method for stability and free vibration analyses of axially functionally graded non-uniform beams resting on constant Winkler-Pasternak elastic foundation. In the proposed novel technique, the power series approximation is first adopted to solve the motion equation. Regarding this numerical methodology, the transverse displacement and all mechanical properties are expanded in terms of power series of a known degree. By solving the eigenvalue problem, one can acquire the fundamental natural frequencies. According to aforementioned method, the expression of vibrational mode shape is also determined. Based on the similarities existing between the vibrational and buckling deformation shapes, Rayleigh-Ritz method is finally employed to construct eigenvalue problem for obtaining the critical loads. In order to illustrate the correctness and convergence of the method, several numerical examples of axially non-homogeneous and homogeneous beams are conducted. The obtained outcomes are compared to the results of Finite Element Analysis in terms of ANSYS software and those of other available numerical and analytical solutions. The accuracy of the method is then remarked.

Laminated composite plates are extensively used in various industries due to their high stiffness-to-weight ratio and directional properties that allow optimization of the stiffness characteristics for specific applications. In multi-objective optimization problems, optimal designs for individual performance metrics may be conflicting, necessitating knowledge on the design requirements for different metrics and potential trade-offs. In this paper, a multi-objective design methodology for laminated composite plates with dynamic and load-carrying requirements is presented. Lamination parameters are used to characterize laminate stiffness matrices in a compact form resulting in a convex design space. Single and multi-objective optimization studies are carried out to determine the optimal stiffness properties. For improving the dynamic performance, maximization of the fundamental frequency metric is aimed. For enhancing the load-carrying capability, buckling load and equivalent stiffness metrics are maximized. Conforming and conflicting behavior of multiple objective functions for different plate geometries, boundary conditions and load cases are presented by determining Pareto-optimal solutions. The results provide a valuable insight for multi-objective optimization of laminated composite plates and show that presented methodology can be used in the design of such structures for improving the dynamic and load-carrying performance., European Union (European Union); H2020; European Union Seventh Framework Programme; FP7-PEOPLE-2012-ITN; Marie Curie Initial Training Network; Aerospace Multidisciplinarity Enabling DEsign Optimization (AMEDEO)

The present work studies the application of a probabilistic methodology in the sensitivity analysis of a steel column to identify the dominant parameters in its load capacity. Monte Carlo type simulations, in combination with the finite element method, was carried out to achieve the proposed objective. The geometric nonlinearity in the model was considered in order to reflect large deflections and initial geometric imperfections. The results show that the sensitivity of the column to a specific input parameter depends on the slenderness ratio and, hence, the column will be more sensitive to one parameter or another depending on that relationship.

The present paper is devoted to the numerical analysis and experimental tests of compressed bars with built-up cross section which are commonly used as a top chord of the roof trusses. The significant impact on carrying capacity for that kind of elements in case of out-of-plane buckling is appropriate choice of battens which are used to provide interaction between separate members. Linear buckling analysis results and nonlinear static analysis results, with material and geometrical nonlinearity, are presented for the bar with built-up cross section which was used as the top chord of the truss made in reality. Diagonals and verticals which are supports for the top chord between marginal joints were replaced by the elastic supports. The threshold stiffness (minimum stiffness) for the intermediate elastic supports which ensures maximum buckling load was appointed for the beam and shell model of the structure. The magnitude of limit load depended on length of the battens was calculated for models with initial geometric imperfections. The experimental tests results for the axially compressed bars with builtup cross section and elastic support are presented.

The paper is devoted to the numerical and experimental research of stability of a truss with side elastic supports at the top chord. The structure is a model of a real roof truss scaled by factor ¼. The linear buckling analysis and non-linear static analysis were carried out. The buckling length factor for the compressed top chord was calculated and the limit load for the imperfect truss shell model with respect to brace stiffness was obtained. The relation between brace normal force and loading of the truss is presented. The threshold stiffness of braces necessary to obtain the maximum buckling load was found. The truss load bearing capacity obtained from numerical analysis was compared with Eurocode 3 requirements.

Determination of buckling behavior of shell structures has long been identified as a challenging task. This is largely because the buckling behavior is masked by local large deformations, which occur once the critical load is reached. This research proposes a novel technique to accurately predict the buckling load of imperfect cylindrical shells using gene expression programming (GEP), which is an evolutionary artificial intelligence method. An existing experimental data bank was employed for training and testing the program, and the obtained buckling load of shell structures were accordingly verified. From the results, it is concluded that GEP is a promising and reliable method to determine the buckling load of shell structures subjected to axial compression.

An analytical approach is presented for the accurate definition of lower and upper bounds for the pull-in voltage and tip displacement of a micro- or nanocantilever beam subject to compressive axial load, electrostatic actuation and intermolecular surface forces. The problem is formulated as a nonlinear two-point boundary value problem and has been transformed into an equivalent nonlinear integral equation. Initially, new analytical estimates are found for the beam deflection, which are then employed for assessing novel and accurate bounds from both sides for the pull-in parameters, taking into account for the effects of the compressive axial load. The analytical predictions are found to closely agree with the numerical results provided by the shooting method. The effects of surface elasticity and residual stresses, which are of significant importance when the physical dimensions of structures descend to nanosize, are also included in the proposed approach.

Throughout this paper, a new system for connecting composite sandwich wall panels is proposed. The relevant structural components are investigated with the aim of utilizing these panels as insulated wall elements in building applications or prefabricated modular systems. The adopted sandwich wall panels are composed of hand-layup Glass Fiber Reinforced Polymer (GFRP) outer skins and low density closed polyurethane (PU) foam core. The sandwich wall panels present an overall geometry of 2880×960×64 mm3. One challenge of the proposed new system that was examined included joining the panels in the longitudinal direction (along their height) and transversally connecting (along their width) to other structural elements, similar to beams at the bottom and top. The structural performance of the sandwich wall panels was experimentally tested and thereafter analytically assessed in two cases: (i) single wall panels; (ii) two jointed wall panels. Outward localized GFRP wrinkling, followed by global buckling was observed as the dominant failure mode in both cases. Further, the capability of the proposed connection system to increase the axial load capacity of the jointed panels was evaluated. The study illustrates that axial capacity of two jointed sandwich wall panels compared to the single sandwich wall panel, increased substantially from 91% to 152% depending on the failure modes., This work is part of the research project ClickHouse - Development of a prefabricated 595 emergency house prototype made of composites materials, involving the company ALTO – 596 Perfis Pultrudidos, Lda., CERis/Instituto Superior Técnico and ISISE/University of Minho, supported by FEDER funds through the Operational Program for Competitiveness Factors – 598 COMPETE and the Portuguese National Agency of Innovation (ADI) - project no. 38967. 599 Special thanks are given to company ALTO who manufactured all the elements (GFRP 600 profiles and sandwich panels) involved in this work. ClickHouse - FEDER / COMPETE / ADI - project no. 38967., info:eu-repo/semantics/publishedVersion

In this work, variational formulations are proposed for solving numerically the problem of bending and buckling of Timoshenko nano-beams. The present work belongs to research branch in which the non-local theory of elasticity has been used for analysis of beam-like elements in smart materials, micro-electro-mechanical (MEMS) or nano-electro-mechanical systems (NEMS). In fact, the local beam theory is not adequate to describe the behavior of beam-like elements of smart materials at the nano-scale, so that different non-local models have been proposed in last decades for nano-beams. The nano-beam model considered in this work is a convex combination (mixture) of local and non-local phases. In the non-local phase, the kinematic entities in a point of the nano-beam are expressed as integral convolutions between internal forces and an exponential kernel. The aim is to construct a functional whose stationary condition provides the solution of the problem. Two different functionals are defined: one for the pure non-local model, where the local fraction of the mixture is absent, and the other for the mixture with both local and non-local phases. The Euler equations of the two functionals are derived; then, attention focuses on the mixture model. The functional of the mixture depends on unknown Lagrange multipliers and the Euler equations of the functional provide not only the governing equations of the problem but also the relationships between these Lagrange multipliers and the other variables on which the functional depends. In fact, approximations of the variables of the functional can not be chosen arbitrarily in numerical analyzes but have to satisfy suitable conditions. The Euler equations involving the Lagrange multipliers are essential in the numerical analyzes and suggest the correct approximations that have to be adopted for Lagrange multipliers and the other unknown variables of the functional. The proposed method is verified by comparing numerical solutions with exact solutions in bending problem. Finally, the method is used to determine the buckling load of Timoshenko nano-beams with mixture of phases.

In this experimental and numerical study, the effect of plate thickness, the diameter of circular cutout, the distance between circular cutouts and rowing orientation angle effect (?) on the buckling load of E-glass/vinylester pultruded composite beams with single and double circular cutouts, were investigated. The composite beam having 2, 4, and 6 mm thicknesses was produced as [Mat/? /Mat/? /Mat] by using pultrusion technique. Seven different fiber angles as 0° , 15° , 30° , 45° , 60° , 75° , and 90° were chosen for investigation of rowing orientation angle. The distances between each circular cutout were selected as 15, 30, 45, 60, and 75 mm in the case of double circular cutouts. The diameters of circular cutouts were chosen as 2, 4, 6, 8, and 10 mm to investigate the effect of cutout size. The experimental buckling loads were compared with the results calculated from the numerical analysis. ANSYS 11 commercial software was used for numerical study. A good agreement was obtained between numerical and experimental results. Copyright © 2014 Techno-Press, Ltd.

In this research, I propose computational morphogenesis which introducedthe restrictions to structural stability for purpose of deciding limits. A buckling load coefficient is adopted as index which measures structural stability. I perform computational morphogenesis using this technique and grasp the characteristic and tendency of a structure form which are acquired.

In this study, the buckling behaviors of E-glass/epoxy composite plates with a central hole in different geometric shapes for different boundary conditions will be analyzed. For the analyzes, ratio between thickness and length of the specimen (L/t = 20, 30, 40, 50) and two different laminae orientation angles such as [0o /90o ] 4 and [(0o /90o )2] S parameters will be considered. The buckling behavior of laminated composite plates subjected to axial compressive load using a finite element method package program such as ANSYS will be analyzed. The analyzes will be carried out for three different boundary conditions: clamped-clamped support, clamped-fixed support and fixed-fixed support. Thus, the L/t ratio and laminae orientation angle effects on the buckling behavior of composite plates for different boundary conditions will be investigated. The obtained analyze results show that different L/t ratios and laminae orientation angles have significant effects on the buckling load of composite plates. In additon, the hole shape also affects the buckling load

© 2017, Allerton Press, Inc. We consider a problem about non-uniformly scaled buckling modes of isolated fiber (without accounting of interaction with the surrounding epoxy) or bundle of fibers, which are structural elements of fiber reinforced plastics under the transverse tension (compression) and shear stresses in prebuckling state. Such initial state is formed in fibers and bundles of fibers at tension-compression tests of flat specimens from cross ply composites with unidirectional fibers. For problem statement we use equations recently constructed by reduction of consistent version of geometrically nonlinear equations of theory of elasticity to one dimensional equations of rectilinear beams. Equations are based on refined shear S. P. Timoshenko model with accounting of tension-compression stresses in transverse directions. We give theoretical explanation of developed phenomenon as reducing shear modulus of elasticity of fiber reinforced plastic during the increasing of shear strains. We show that under the loading process of specimens under review uninterruptedly structure reconstruction of composite trough implementation and uninterruptedly changing of internal buckling modes at changing wave parameter is feasible.

In this study, the buckling behavior of E-glass/epoxy, E-glass/polyester and E-glass/vinylester based composite plates with fiber orientation of [0o /90o ] 4 will be determined experimentally. Test specimens prepared according to the ASTM standards. All buckling tests were performed using a Shimadzu brand tensile machine with load capacity of ± 250 kN. Some of the specimens consist hole and some do not. The specimens with hole have different geometrical shapes and also same hole area. The specimens were subjected to axial compressive load until buckling failure occurred. From the obtained test results, it was shown that the hole geometry and matrix materials have significant effects on the buckling load of the laminated composite plates.

The fire resistance of partially encased columns depends on the temperature evolution during fire exposure. This work aims to evaluate the effect of the balanced summation model on the design of the buckling load of Partially Encased Columns under fire situation. New improvements will be presented to assess fire resistance, suggesting some modification in the Annex G of Eurocode EN 1994-1-2. The advanced calculation method presented herein is based on the 3D modelling of the Partially Encased Column, using steel profiles ranging from IPE200 to IPE500 and HEB160 to HEB500, and using different buckling lengths. An incremental and interactive procedure is used to solve the geometric and material non-linear behaviour. The temperature effect is taken into account, using the uncouple thermal-structural analysis. The results obtained by the numerical simulations are in good agreement with the new simple calculation method and are also useful to prescribe the buckling curve that best fits the 3D simulation results. A resistência ao fogo de pilares parcialmente revestidos com betão, dependem da evolução da temperatura durante o tempo de exposição ao fogo. Este trabalho visa avaliar o efeito do Método da Soma Pesada na conceção da carga resistente à encurvadura de pilares parcialmente revestidos em situação de incêndio, de acordo com as normas europeias. Serão apresentadas novas formulações para avaliar a resistência ao fogo, no qual se sugere alterações de alguns aspetos prescritos no Anexo G do Eurocode EN 1994-1-2. O método avançado de cálculo apresentado nesta tese é baseado na modelação 3D da coluna parcialmente revestida, utilizando perfis estruturais na gama compreendida desde IPE200 ao IPE500 e HEB160 ao HEB500, e usando diferentes comprimentos de encurvadura. Um processo incremental e interativo é utilizado para resolver um problema não lienar geométrico e material.. O efeito da temperatura é considerado utilizando a análise sem acoplamento termo-estrutural. Os resultados obtidos pelas simulações numéricas serão utilizados para comparar com os valores do método de cálculo simplificado e também será útil para prescrever uma curva de flexão que melhor se adeque para os resultados das simulações em 3D.

ResumenEn este trabajo se aplica un procedimiento basado en el concepto de Acción Repartida Equivalente (ARE) al análisis, por el Método de Elementos Finitos (MEF) formulado en desplazamientos y solución nodal exacta, de pilares con deformación por cortante de acuerdo con la teoría de Timoshenko. Los resultados obtenidos con la metodología ARE-MEF, en los casos analizados, ponen de manifiesto que con un número muy reducido de elementos (uno y dos en los ejemplos desarrollados) se alcanza gran exactitud en desplazamientos, giros y esfuerzos. Sin embargo con otras metodologías formuladas en desplazamientos, como por ejemplo la de integración reducida, se requiere del orden de 40 elementos para alcanzar resultados similares. Asimismo en el presente trabajo, a partir del MEF con solución nodal exacta se determinan de una forma directa y sistemática las funciones de estabilidad y la carga de pandeo para el pilar de Timoshenko.AbstractThis paper describes a procedure based on the concept of Equivalent Distributed Loads (EDL) applied to the Finite Elements Method (FEM) based on displacements and exact nodal solution of columns subject to shear deformation in accordance with the Timoshenko beam theory. The results obtained using this “EDL-FEM” methodology, in the cases studied, show that a high level of exactness in displacements, rotations as well as shear force and bending moment is obtained with a very small number of elements (one or two in the examples developed). Other methodologies based on displacements, such as reduced integration, require on the order of 40 elements to achieve similar results. The stability functions and buckling load for the Timoshenko beam are also determined in a direct and systematic way from the FEM with exact nodal solution.

The single-layer lattice shell is one of the lightest and the slimmest structure systems constructing domes. However, as it has particularly law bending rigidity, the overall buckling is the fatal problem. The analysis object of this paper is the hybrid shell which is the perpendicularly gridded wooden single-layer lattice shell with supplementary parts inserted. And the analysis is operated at several conditions to determine the optimum arrangement of the supplementary parts using genetic algorithm (GA) as the determination method. The objective of this paper is to clarify the effect of the variation of the rigidity of joint on the optimum arrangement and the effectiveness of supplement against buckling.

The Imperialist Competitive Algorithm (ICA) that was recently introduced has shown its good performance in optimization problems. In this paper, a novel optimization algorithm based on ICA is used for optimizing the generalized formulation of critical buckling load on plates made of Functionally Graded Materials (FGMs) with variation in thickness. The formulation, which is applicable to thin Functionally Graded (FG) plates, can also be used to analyze and optimize FGMs in each layer of the plates. At last, the results of ICA are compared with those obtained from Genetic Algorithm (GA). The outcome shows the success of ICA in optimizing the buckling load of FG plates.