EM - Escola de Minas

URI permanente desta comunidadehttp://www.hml.repositorio.ufop.br/handle/123456789/6

Notícias

A Escola de Minas de Ouro Preto foi fundada pelo cientista Claude Henri Gorceix e inaugurada em 12 de outubro de 1876.

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2007 - 200922010 - 201972020 - 20211

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Autor: search.filters.author.Gonçalves, Paulo Batista

Resultados da Pesquisa

Agora exibindo 1 - 10 de 10
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    Closed-form solutions for the symmetric nonlinear free oscillations of pyramidal trusses.
    (2021) Santana, Murillo Vinícius Bento; Gonçalves, Paulo Batista; Silveira, Ricardo Azoubel da Mota
    This work presents the development of analytical solutions regarding the symmetric free vibrations of pyramidal trusses, considering a general large strain measure. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. Illustrative examples considering the quadratic (Green–Lagrange) and logarithmic (Hencky) strain measures are used to exemplify the influence of the strain measure on the results. Pyramidal trusses are well-known bistable structures and in the unloaded configurations may present different analytical solutions depending on the initial conditions: small amplitude vibrations around each stable equilibrium configuration or large cross-well vibrations. These families of solution are separated by two homoclinic orbits, constituting the boundaries of the two potential wells, which are related to the saddle point initial conditions. In addition, closed-form time solutions for the undamped vibrations are derived and the nonlinear frequency–amplitude relations, which are a measure of the degree and type of nonlinearity (hardening or softening), are obtained. Finally, a semi-analytical procedure for the damped vibrations is also constructed.
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    An efficient strategy for solving structural nonlinear equations by combining the orthogonal residual method and normal flow technique.
    (2019) Maximiano, Dalilah Pires; Silveira, Ricardo Azoubel da Mota; Silva, Andréa Regina Dias da; Gonçalves, Paulo Batista
    This paper presents a new procedure for solving structural nonlinear problems by combining the orthogonal residual method (ORM) and normal flow technique (NFT). The perpendicularity condition to the Davidenko flow, introduced by the NFT, which must be satisfied during the iterative process, overcome the difficulties, i.e. the poor convergence and inefficiency of the ORM close to the limit points, particularly the displacement limit points (snap-back behavior). Basically, the idea of the proposed strategy is to adjust the load parameter, which is treated as a variable in the nonlinear incremental-iterative solution process, assuming that the unbalanced forces (residual forces) must be orthogonal to the incremental displacements. This constraint is used together with the NFT perpendicularity condition. The proposed procedure is tested, and its efficiency is corroborated through the analyses of slender shallow and nonshallow arches and an L-frame since they exhibit highly nonlinear behaviors under certain loading conditions. It is concluded that the proposed procedure can overcome the numerical instability problems in the neighborhood of critical points when using only the conventional OR process, and the procedure compares favorably with the arc-length method, minimum residual displacement method, and generalized displacement control method.
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    Stability and load capacity of an elasto-plastic pyramidal truss.
    (2019) Santana, Murillo Vinícius Bento; Gonçalves, Paulo Batista; Silveira, Ricardo Azoubel da Mota
    The present work investigates, using a corotational finite element formulation considering large displacements and rotations, geometric imperfections and an elasto-plastic material constitutive law, the nonlinear behavior of a pyramidal space truss under vertical and horizontal loads. Additionally novel analytical closed-form solutions for the nonlinear equilibrium paths, natural frequencies and critical parameters are derived for comparison purposes and investigation of the influence of geometric and material parameters on the truss stability. This geometry has an immediate practical interest since these structures are currently used in many present-day applications, either as main structural component or as a constitutive element. Four types of nonlinear instability phenomena are investigated theoretically and numerically: saddle-node (limit point) bifurcation, pitchfork bifurcation, individual Eulerian bars buckling and elasto-plastic buckling. Through a detailed parametric analysis the interaction between these buckling phenomena, using the FE tool, is investigated. In addition, the effect of elastic supports is considered. The influence of these phenomena on the load carrying capacity of the structure and its imperfection sensitivity is duly discussed in the present work. Finally, a detailed parametric analysis of a large roof composed of pyramidal truss units is conducted and the influence of the geometric parameters on its bistable behavior and load carrying capacity is investigated.
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    Nonlinear oscillations and dynamic stability of an elastoplastic pyramidal truss.
    (2019) Santana, Murillo Vinícius Bento; Gonçalves, Paulo Batista; Silveira, Ricardo Azoubel da Mota
    Pyramidal space trusses are currently used in many present-day engineering applications, either as main parts or as a constitutive element. The present work studies, using a corotational finite element formulation considering large displacements and rotations and an elastoplastic material behavior with isotropic strain hardening, the nonlinear dynamic behavior of a pyramidal space truss. A bilinear hysteretic model with kinematic hardening is used to represent the material nonlinearity. An appropriate strain measure in such processes is the logarithmic strain. However, the engineering strain and the quadratic strain measures have been usually used to perform the elastic stability analysis of such structures. Thus, in the present work results using both the quadratic and the logarithmic strain measures are compared. First, the static nonlinear behavior is investigated in order to understand the influence of nonlinearities and static preload on the potential energy landscape, which controls the dynamics of the truss. These structures exhibit a two-well potential function that leads to coexisting in-well and cross-well solution branches, resulting in several coexisting periodic, quasi-periodic and chaotic attractors. The influence of the constitutive law, strain measure, truss geometry and support flexibility on the static stability is then investigated. Based on these results, a detailed parametric analysis of the nonlinear truss response under vertical load is conducted using bifurcations diagrams of the Poincaré map to investigate the effect of the constitutive law, strain measure, truss geometry and load control parameters on the bifurcation scenario, coexisting attractors and dynamic buckling loads. The effect of the strain hardening parameter is particularly emphasized, allowing a more comprehensive picture of the dynamical behavior exhibited by the bistable system. Properties of the response are further illustrated by samples of time and phase plane responses and the related Poincaré section plots. In addition to known behaviors, a rich class of solutions and bifurcations, including jump phenomena, symmetry-breaking, period-doubling cascades, fold and chaos is detected.
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    On the nonlinear transient analysis of planar steel frames with semi-rigid connections : from fundamentals to algorithms and numerical studies.
    (2018) Silva, Andréa Regina Dias da; Batelo, Everton André Pimentel; Neves, Francisco de Assis das; Gonçalves, Paulo Batista
    This paper presents the fundamentals for prediction of a more realistic behavior of planar steel frames with semi-rigid connections under dynamic loading. The majority of the research in this area concentrates on the nonlinear static analysis of frames with semi-rigid connections. Indeed, few studies have contributed to the nonlinear dynamic and vibration analyses of frames. Therefore, this article first describes the frames’ semi-rigid connection behavior under monotonic and cyclic loads, and presents the independent hardening technique adopted to simulate the joint behavior under cyclic excitation. In a finite element context, this paper presents an efficient numerical methodology that is proposed in algorithmic form to obtain the nonlinear transient response of the structural system. The paper also presents, in algorithmic form, a complete description of the adopted connection hysteretic model. Satisfying the equilibrium and compatibility conditions, and assuming only the connection’s rotational deformation due to bending as variable, this work obtains the tangent stiffness and mass matrices of the beam-column element with semi-rigid connections at the ends. The study concludes by verifying and validating the proposed numerical approach using four structural steel systems: a L-frame, a two-story frame, a six-story frame, and a four-bay five-story frame. The analyses show that the hysteresis of the semi-rigid connection has a strong effect on the frames’ responses and is an important source of damping during the structural vibration.
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    Nonlinear resonance analysis of slender portal frames under base excitation.
    (2017) Muñoz, Luis Fernando Paullo; Gonçalves, Paulo Batista; Silveira, Ricardo Azoubel da Mota; Silva, Andréa Regina Dias da
    The dynamic nonlinear response and stability of slender structures in the main resonance regions are a topic of importance in structural analysis. In complex problems, the determination of the response in the frequency domain indirectly obtained through analyses in time domain can lead to huge computational effort in large systems. In nonlinear cases, the response in the frequency domain becomes even more cumbersome because of the possibility of multiple solutions for certain forcing frequencies. Those solutions can be stable and unstable, in particular saddle-node bifurcation at the turning points along the resonance curves. In this work, an incremental technique for direct calculation of the nonlinear response in frequency domain of plane frames subjected to base excitation is proposed. The transformation of equations of motion to the frequency domain is made through the harmonic balance method in conjunction with the Galerkin method. The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves. Suitable examples are presented, and the influence of the frame geometric parameters and basemotion on the nonlinear resonance curves is investigated.
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    Constrained and unconstrained optimization formulations for structural elements in unilateral contact with an elastic foundation.
    (2007) Silveira, Ricardo Azoubel da Mota; Pereira, Wellington Luís Assis; Gonçalves, Paulo Batista
    In this work, two numerical methodologies are proposed for the solution of unilateral contact problems between a structural member (beam or arch) and an elastic foundation. In the first approach, the finite element method is used to discretize the structure and elastic foundation and the contact problem is formulated as a constrained optimization problem. Only the original variables of the problem are used, subjected to inequality constraints, and the relevant equations are written as a linear complementary problem (LCP). The second approach is based on the Ritz method, where the coordinates defining the limits of the contact regions are considered as additional variables of the problem. The contact problem here is treated as an unconstrained optimum design problem. These proposed methodologies are then tested and compared using results from specific problems involving structures under unilateral contact constraints.
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    Nonlinear analysis of structural elements under unilateral contact constraints by a Ritz type approach.
    (2008) Silveira, Ricardo Azoubel da Mota; Pereira, Wellington Luís Assis; Gonçalves, Paulo Batista
    A nonlinear modal solution methodology capable of solving equilibrium and stability problems of uni-dimensional structural elements (beams, columns and arches) with unilateral contact constraints is presented in this work. The contact constraints are imposed by an elastic foundation of the Winkler type, where special attention is given to the case in which the foundation reacts in compression only, characterizing the contact as unilateral. A Ritz type approach with moveable boundaries, where the coordinates defining the limits of the contact regions are considered as additional variables of the problem, is proposed to solve this class of unilateral contact problems. The methodology is illustrated by particular problems involving beams, beam-columns and arches, and the results are compared with available results obtained by finite element and mathematical programming techniques. It is concluded that the Ritz type approach proposed is particularly suited for the analysis of structural problems where the number, but not the length, of the contact regions between the bodies are known a priori. Therefore, it can substitute in these cases finite element applications and be used as a benchmark for more general and complex formulations as well.
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    Nonlinear dynamic behavior and instability of slender frames with semi-rigid connections.
    (2010) Galvão, Alexandre da Silva; Silva, Andréa Regina Dias da; Silveira, Ricardo Azoubel da Mota; Gonçalves, Paulo Batista
    The free and forced nonlinear vibrations of slender frames with semi-rigid connections are studied in this work. Special attention is given to the influence of static pre-load on the natural frequencies and mode shapes, nonlinear frequency–amplitude relations, and resonance curves. An efficient nonlinear finite element program for buckling and vibration analysis of slender elastic frames with semi-rigid connections is developed. The equilibrium paths are obtained by continuation techniques, in combination with the Newton-Raphson method. The ordinary differential equations of motion of the discretized frame are solved by the Newmark implicit numerical integration method using adaptive time-step strategies. Three structural systems with important practical applications are analyzed: an L-frame, a shallow arch, and a pitched-roof frame. The results highlight the importance of the static pre-load and the stiffness of the semi-rigid connections on the buckling and vibration characteristics of these structures.
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    A numerical approach for equilibrium and stability analysis of slender arches and rings under contact constraints.
    (2013) Silveira, Ricardo Azoubel da Mota; Nogueira, Christianne de Lyra; Gonçalves, Paulo Batista
    Underground constructions, such as shafts, courtain walls, foundations, pipes and tunnels, use structural elements that are supported by a geological medium (soil or rock) or are used to support the geological medium loads. If the geological medium is unable to react under tension, the structural element is subjected to unilateral contact constraints and, during the deformation process, may loose contact with the surrounding medium at one or more regions. The present work proposes an alternative numerical methodology for the geometrically nonlinear analysis of structural systems under unilateral contact constraints. The nonlinear problem involves two different types of variables: the displacement field and the length and position of the contact regions. In order to solve the resulting algebraic nonlinear equations with contact constraints and obtain the structural equilibrium configuration, the present work proposes a two-level iteration solution strategy at each load step. The first solves the contact problem as a linear complementary problem using Lemke’s algorithm. The second updates the displacement field. A nonlinear beam-column element is used to model the structure, while a bed of springs is used to model the geological medium. The use of an updated Lagrangian formulation, together with continuation and optimization techniques minimize the errors along the equilibrium paths and enables one to trace convoluted non-linear equilibrium paths with a varying number of contact regions. Special attention is given to the behavior of curved unidimensional support systems such as arches and rings. The nonlinear behavior of four such support systems is studied. The results clarify the influence of the foundation position (above or below the structure) and its stiffness on the nonlinear behavior and stability of curved structures. Comparison of the present results with those found in literature demonstrates the accuracy and versatility of the proposed numerical strategy in the analysis of structural elements with unilateral contact constraints.