Buckling analysis of singly curved shallow bi-layered arch under concentrated loading

Bi-layered materials are a reduced weight derivative of the sandwich structure and are comprised of one thin skin face reinforced by a thick layer of low density material. Bi-layered materials are characterized by high flexural stiffness and are a viable alternative to conventional sandwich materials in applications where the functional requirements can be met without the second face sheet of the sandwich. For structural applications bi-layered materials are required to have oil canning and buckling resistance. This work addresses the buckling of shallow bi-layered arches using numerical and analytical approaches. A numerical, finite element model is developed to simulate the buckling phenomenon and the results were compared with known experimental data. An analytical model was developed using the energy method analysis and the buckling load was predicted from the minimum energy criterion. Comparison of the numerical and analytical results yielded fairly good agreement. An imperfection analysis conducted by means of the numerical model indicated that the load carrying capacity of bi-layered structures is reduced by up to 40% due to the presence of material and geometric imperfections. A parametric study conducted using the analytical model has been described to setup design guidelines for shallow bi-layered arches. It was found that the use of bi-layered structures can result in weight reduction of around 70% when compared with equivalent single layered structure

In-plane thermo-mechanical behavior of curved steel beams with constant curvature

Mestrado de dupla diplomação com a UTFPR - Universidade Tecnológica Federal do ParanáCurved steel beams and arches are structures originated from mechanical processes of curving straight members, usually I or H profiles, in order to get a desired geometry to attend aesthetics or project requirements. This type of elements behave differently when compared to regular straight members, with specific instability modes and different responses to various types of loading conditions. For these reasons, such structural members may react distinctively when submitted to fire conditions or elevated temperatures. This paper studies the stability and collapse load of steel curved beams and arches, curved by their major axes, through numerical Finite Element analyses for in-plane buckling at natural and elevated temperatures, simulating a fire event. Firstly, it was developed an analytical method to compute the internal forces based in energy methods for pin-supported arches under two point loads applied at one fourth of the length measured from the supports. Subsequently, linear elastic and nonlinear elasto-plastic buckling and ultimate load analyses were performed at both natural and elevated temperature conditions with the ANSYS Mechanical APDL Finite Element software package, for a variety of span and rise-to-span ratio values, support conditions and steel classes. These results were then compared to critical buckling load formulations found in the literature and to simplified methods presented in Eurocode 3 for elements under bending moments and axial forces. It is seen that support conditions play an important role in the thermo-mechanical response of steel arches, where fixed supports yielded much higher critical load results for every geometry and temperature case. However, even though superior steel classes provide higher resistant loads, regarding responses to thermal loads it was found that support condition is also more significant in this case. Moreover, the standard Eurocode 3 methodology for straight members was compared to the numerical results, which showed a good fit for lower bound loads except for higher slendernesses under elevated temperatures, where numerical solutions yielded result points under the standard resistance curves. Also, an analytical and experimental study on the cold-curving process of straight steel beams into arches using point loads was conducted, aiming to analytically define a post-curving residual stress profile and investigate the influence of elastic springback in the final shape of an arch.Vigas curvas e arcos de aço são estruturas originadas de processos mecânicos de curvamento de membros retos em curvos, geralmente perfis I ou H, a fim de obter a geometria desejada para atender a requisitos estéticos ou de projeto. Esse tipo de elemento comporta-se de maneira diferente quando comparado a membros retos regulares, com modos de instabilidade específicos e respostas diferentes a várias condições de carregamento. Por esses motivos, esses membros estruturais podem também reagir diferentemente quando submetidos a condições de incêndio ou temperaturas elevadas. Este trabalho estuda a estabilidade e a carga de colapso de vigas e arcos curvos de aço, curvados em seus eixos de maior resistência, através de análises numéricas de elementos finitos para encurvadura no plano à temperaturas ambiente e elevadas, simulando um evento de incêndio. Primeiramente, foi desenvolvido um método analítico para calcular as forças internas baseadas em métodos de energia para arcos bi-rotulados sob cargas pontuais aplicadas em um quarto do comprimento medido a partir dos suportes. Posteriormente, foram realizadas análises de encurvadura linear elástica e de carga última não-linear elasto-plástica em condições de temperatura naturais e elevada com o pacote de software ANSYS Mechanical APDL de elementos finitos, para uma variedade de valores de vão e relação altura-vão, condições de suporte e classes de aço. Esses resultados foram comparados com as formulações de carga crítica de encurvadura encontradas na literatura e com os métodos simplificados apresentados no Eurocódigo 3 para elementos submetidos a momentos fletores e forças axiais. Observa-se que as condições de suporte desempenham um papel importante na resposta termomecânica dos arcos de aço, onde os suportes fixos produzem resultados de carga crítica muito mais altos para cada caso de geometria e temperatura. Ademais, embora classes de aço superiores proporcionem maior resistência mecânica, em relação às respostas à cargas térmicas, verificou-se que a condição de suporte também é mais significativa neste caso. Além disso, a metodologia padrão do Eurocódigo 3 para membros retos foi comparada com os resultados numéricos, que mostraram um bom ajuste com os limites impostos pela metodologia padrão, exceto para esbeltezas mais altas sob temperaturas elevadas, onde as soluções numéricas produziram resultados abaixo das curvas de resistência padrão. Também, um estudo experimental e analítico foi conduzido acerca do processo de curvamento a frio de vigas de aço retas em arcos utilizando cargas concentradas, com objetivo de definir analiticamente um perfil de tensões residuais póscurvamento e investigar a influência do retorno elástico na forma final de um arco

Stability of Pseudo-Funicular Elastic Grid Shells

International audienceThe paper presents some results on the influence of the pre-stress induced by the erection method of elastic grid shells on their buckling capacity. It starts with the numerical methods and their validation with the study of a prebuckled arch. Then, a form-finding scheme using low-speed dynamics is used to generate automatically a family of elastic grid shells, and their buckling capacity is compared to the one of grid shells with the exact same geometry, but without any pre-stress. The paper demonstrates finally that the pre-stress decreases by a few percent the buckling capacity of elastic grid shells

In-Plane Stability of Fixed-Fixed Heterogeneous Curved Beams under a Concentrated Radial Load at the Crown Point

The paper by Kiss and Szeidl (2014) is devoted to the stability problem of pinned-pinned shallow curved beams provided that the beam is made of a heterogeneous material and the radius of curvature is constant. The present paper is concerned with the same issue given that the beam is fixed-fixed. Making use of the model presented in Kiss and Szeidl (2014) we aim to (a) determine the critical value of the central load (applied at the crown point) and (b) compare the results with those valid for homogeneous curved beams

Review of Applications of Nonlinear Normal Modes for Vibrating Mechanical Systems

International audienceThis paper is an extension of the previous review Nonlinear Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments done by the authors, and it is devoted to applications of nonlinear normal modes (NNMs) theory. NNMs are typical regimes of motions in wide classes of nonlinear mechanical systems. The significance of NNMs for mechanical engineering is determined by several important properties of these motions. Forced resonances motions of nonlinear systems occur close to NNMs. Nonlinear phenomena, such as nonlinear localization and transfer of energy, can be analyzed using NNMs. The NNMs analysis is an important step to study more complicated behavior of nonlinear mechanical systems. This review focuses on applications of Kauderer–Rosenberg and Shaw–Pierre concepts of nonlinear normal modes. The Kauderer–Rosenberg NNMs are applied for analysis of large amplitude dynamics of finite-degree-of-freedom nonlinear mechanical systems. Systems with cyclic symmetry, impact systems, mechanical systems with essentially nonlinear absorbers, and systems with nonlinear vibration isolation are studied using this concept. Applications of the Kauderer–Rosenberg NNMs for discretized structures are also discussed. The Shaw–Pierre NNMs are applied to analyze dynamics of finite-degree-of-freedom mechanical systems, such as floating offshore platforms, rotors, piece-wise linear systems. Studies of the Shaw–Pierre NNMs of beams, plates, and shallow shells are reviewed, too. Applications of Shaw–Pierre and King–Vakakis continuous nonlinear modes for beam structures are considered. Target energy transfer and localization of structures motions in light of NNMs theory are treated. Application of different asymptotic methods for NNMs analysis and NNMs based model reduction are reviewed

Recent Developments in the Dynamic Stability of Elastic Structures

Dynamic instability in the mechanics of elastic structures is a fascinating topic, with many issues still unsettled. Accordingly, there is a wealth of literature examining the problems from different perspectives (analytical, numerical, experimental etc.), and coverings a wide variety of topics (bifurcations, chaos, strange attractors, imperfection sensitivity, tailor-ability, parametric resonance, conservative or non-conservative systems, linear or nonlinear systems, fluid-solid interaction, follower forces etc.). This paper provides a survey of selected topics of current research interest. It aims to collate the key recent developments and international trends, as well as describe any possible future challenges. A paradigmatic example of Ziegler's paradox on the destabilizing effect of small damping is also included

On the connection of isolated branches of a bifurcation diagram: the truss arch system

International audienceOne of the important basic issues of bifurcation theory is the determination of the set of the fixed points of non linear evolution equations as a function of its parameters. The branching of branches of solutions rarely occurs in real applications for which imperfections tend to distort these sharp transitions. Furthermore, bifurcation theory may a priori indicate that there are disjoint branches of solutions. In the present work, the truss arch system is considered and described. The bifurcation diagram is carried out numerically. It is shown that the truss arch system is a simple example of coexistence of disjoint branches. Moreover, it is shown that the emergence of the subcritical bifurcations of the non-shallow configuration is the result of the connection of these disjoint branches. The analytic solutions are derived and the connection of the branches is studied