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H. A. F. A. Santos - One of the best experts on this subject based on the ideXlab platform.
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A novel updated Lagrangian Complementary Energy-based formulation for the elastica problem: force-based finite element model
Acta Mechanica, 2014Co-Authors: H. A. F. A. SantosAbstract:This paper addresses the development of a novel updated Lagrangian variational formulation and its associated finite element model for the geometrically nonlinear quasi-static analysis of cantilever beams. The formulation is based on an incremental Complementary Energy principle. The proposed finite element model only contains nodal bending moments as degrees of freedom. The model is used for the analysis of problems modeled by the so-called elastica theory. Numerical solutions satisfying all equilibrium equations in a strong sense can be obtained for arbitrarily large displacements and rotations. A Newton–Raphson method is adopted to trace the post-buckling response. Numerical results are presented and compared with those produced by the standard total Lagrangian two-node displacement-based finite element model.
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A Complementary-Energy based criterion for the stability analysis of geometrically exact framed structures
Computers & Structures, 2012Co-Authors: H. A. F. A. SantosAbstract:Stability analysis is a crucial aspect of structural design, particularly for beam type structures. This paper addresses the development of a Complementary-Energy based (dual) stability criterion for the quasi-static analysis of three-dimensional framed structures modeled using the so-called geometrically exact (Reissner-Simo) beam theory. The criterion is derived from the well known primal stability criterion based on the condition of minimum total potential Energy. This is accomplished by resorting to the Lagrangian multiplier method together with the Legendre transformation. Several numerical benchmark problems are analyzed. The analyses are carried out using two dual finite element models and their corresponding stability criteria, namely, the traditional two-node displacement/rotation-based model with the primal stability criterion, and a recently introduced equilibrium-based model with the proposed dual stability criterion.
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Complementary-Energy Methods for Geometrically Non-linear Structural Models: An Overview and Recent Developments in the Analysis of Frames
Archives of Computational Methods in Engineering, 2011Co-Authors: H. A. F. A. SantosAbstract:Boundary-value problems in solid mechanics are often addressed, from both theoretical and numerical points of view, by resorting to displacement/rotation-based variational formulations. For conservative problems, such formulations may be constructed on the basis of the Principle of Stationary Total Potential Energy. Small deformation problems have a unique solution and, as a consequence, their corresponding total potential energies are globally convex. In this case, under the so-called Legendre transform, the total potential Energy can be transformed into a globally concave total Complementary Energy only expressed in terms of stress variables. However, large deformation problems have, in general, for the same boundary conditions, multiple solutions. As a result, their associated total potential energies are globally non-convex. Notwithstanding, the Principle of Stationary Total Potential Energy can still be regarded as a minimum principle, only involving displacement/rotation fields. The existence of a maximum Complementary Energy principle defined in a truly dual form has been subject of discussion since the first contribution made by Hellinger in 1914. This paper provides a survey of the Complementary Energy principles and also accounts for the evolution of the Complementary-Energy based finite element models for geometrically non-linear solid/structural models proposed in the literature over the last 60 years, giving special emphasis to the Complementary-Energy based methods developed within the framework of the geometrically exact Reissner-Simo beam theory for the analysis of structural frames.
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On a pure Complementary Energy principle and a force-based finite element formulation for non-linear elastic cables
International Journal of Non-Linear Mechanics, 2011Co-Authors: H. A. F. A. Santos, C.i. Almeida PauloAbstract:Abstract A Complementary-dual force-based finite element formulation is proposed for the geometrically exact quasi-static analysis of one-dimensional hyperelastic perfectly flexible cables lying in the two-dimensional space. This formulation employs as approximate functions the exact statically admissible force fields, i.e. , those that satisfy the equilibrium differential equations in strong form, as well as the equilibrium boundary conditions. The formulation relies on a principle of total Complementary Energy only expressed in terms of force fields, being therefore called a pure principle. Under the assumption of stress-unilateral behavior, this principle can be regarded as being dual to the principle of minimum total potential Energy, corresponding therefore to a maximum principle. Some numerical applications, including cables suspended from two and three points at the same level or at different levels, with both Hookean and Neo-Hookean material behaviors, are presented. As it will be shown, in contrast to the standard two-node displacement-based formulation derived from the principle of minimum total potential Energy, the proposed dual force-based formulation is capable of providing the exact solution of a given problem only using a single finite element per cable. Both the proposed principle of pure Complementary Energy and its corresponding force-based finite element formulation can be easily extended to the case of cables lying in the three-dimensional space.
Yijiang Peng - One of the best experts on this subject based on the ideXlab platform.
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Complementary Energy Principle on Base Forces
Advances in the Base Force Element Method, 2019Co-Authors: Yijiang Peng, Yinghua LiuAbstract:The Complementary Energy principle is the foundation of the base forces element method. In the references (Gao in Science in China: Series G Physics, Mechanics and Astronomy 49:341–356, 2006), Gao put forward a Complementary Energy principle for the problem of large elastic deformation. The form of the Complementary Energy principle is the same as that of the small deformation case. In recent years, some scholars have studied Gao’s Complementary Energy principle and put forward some generalized Complementary Energy principles. In this chapter, we will introduce Gao's Complementary Energy principle.
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A Degenerated Plane Truss Model of Base Force Element Method on Complementary Energy Principle
International Journal of Computational Methods, 2018Co-Authors: Yijiang Peng, Xinxin Yang, Ruixue LiAbstract:In order to study the performance of base force element method (BFEM), a new 2-node degenerated plane element model based on the BFEM of Complementary Energy principle is presented for linear elasticity problem and geometrically nonlinear problem respectively in this paper. The plane truss element model can easily be obtained by degenerating from a four-mid-node plane element of the BFEM based on Complementary Energy principle for linear elasticity problem or geometrically nonlinear problem. The compliance matrix of the rod element model is same as the compliance matrix of the four-mid-node plane element of the BFEM. According to the characteristics of analysis for truss structure, the nodal equilibrium conditions and the displacement coordination conditions of each rod at the nodes have been considered when the compliance matrix of structure is integrated. In order to verify the feasibility of the degenerated plane element model, several truss problems are analyzed and their solutions are compared to the analytical solutions and the numerical results which are calculated with the traditional displacement FEM. It is found that the model has shown high precision and good performance.
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A Degenerated Plane Truss Model of Base Force Element Method on Complementary Energy Principle
International Journal of Computational Methods, 2017Co-Authors: Yijiang Peng, Xinxin Yang, Ruixue LiAbstract:In order to study the performance of base force element method (BFEM), a new 2-node degenerated plane element model based on the BFEM of Complementary Energy principle is presented for linear elasticity problem and geometrically nonlinear problem respectively in this paper. The plane truss element model can easily be obtained by degenerating from a four-mid-node plane element of the BFEM based on Complementary Energy principle for linear elasticity problem or geometrically nonlinear problem. The compliance matrix of the rod element model is same as the compliance matrix of the four-mid-node plane element of the BFEM. According to the characteristics of analysis for truss structure, the nodal equilibrium conditions and the displacement coordination conditions of each rod at the nodes have been considered when the compliance matrix of structure is integrated. In order to verify the feasibility of the degenerated plane element model, several truss problems are analyzed and their solutions are compared to the...
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Application of Base Force Element Method on Complementary Energy Principle to Rock Mechanics Problems
Mathematical Problems in Engineering, 2015Co-Authors: Yijiang Peng, Qing Guo, Zhaofeng Zhang, Yanyan ShanAbstract:The four-mid-node plane model of base force element method (BFEM) on Complementary Energy principle is used to analyze the rock mechanics problems. The method to simulate the crack propagation using the BFEM is proposed. And the calculation method of safety factor for rock mass stability was presented for the BFEM on Complementary Energy principle. The numerical researches show that the results of the BFEM are consistent with the results of conventional quadrilateral isoparametric element and quadrilateral reduced integration element, and the nonlinear BFEM has some advantages in dealing crack propagation and calculating safety factor of stability.
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A 4-Mid-Node Plane Model of Base Force Element Method on Complementary Energy Principle
Mathematical Problems in Engineering, 2013Co-Authors: Yinghua Liu, Yijiang Peng, Lijuan Zhang, Qing GuoAbstract:Using the base forces as fundamental variables to describe the stress state and the displacement gradients that are the conjugate variables of the base forces to describe the deformation state for the two-dimensional elasticity problems, a 4-mid-node plane model of base force element method (BFEM) based on Complementary Energy principle is proposed. In this paper, the Complementary Energy of an element of the BFEM is constructed by using the base forces. The equilibrium conditions are released by the Lagrange multiplier method, and a modified Complementary Energy principle described by the base forces is obtained. The formulation of the 4-mid-node plane element of the BFEM is derived by assuming that the stress is uniformly distributed on each edge of the plane elements. A procedure of the BFEM on Complementary Energy principle is developed using MATLAB language. The numerical results of examples show that this model of the BFEM has high precision and is free from mesh sensitivity. This model shows good performances.
Magdi Mohareb - One of the best experts on this subject based on the ideXlab platform.
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Complementary Energy Based Formulation for Torsional Buckling of Columns
Journal of Engineering Mechanics, 2009Co-Authors: R. Emre Erkmen, Magdi Mohareb, M.a. BradfordAbstract:A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary Complementary Energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in Complementary Energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, Complementary Energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary Complementary Energy is considered for the elastic torsional buckling analysis of columns. The Complementary Energy expression is obtained from the well known total potential Energy functional by using Frederichs’ transformation. In contrast to flexural b...
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Buckling analysis of thin-walled open members—A Complementary Energy variational principle
Thin-Walled Structures, 2008Co-Authors: R. Emre Erkmen, Magdi MoharebAbstract:This first of two companion papers develops a new variational principle for the buckling analysis of thin-walled members based on the principle of stationary Complementary Energy. Some of the aspects of the Vlasov thin-walled beam theory (the rigid cross section assumption, and the stress expressions) are postulated to describe the behavior of members while other aspects of the theory (i.e., the zero shear strain assumption at mid-surface) are discarded. Koiter's formulation based on polar decomposition theory in finite elasticity is adopted to formulate expressions for statically admissible stress resultant fields. The stationarity conditions of the Complementary Energy expression are then evoked to yield the conditions of neutral stability and associated boundary conditions in which the rotation fields appear explicitly. The formulation seamlessly incorporates shear deformation effects and load position effects. Also, the Wagner effect and the mono-symmetry property which arise in displacement based formulations arise in the present formulation in a natural way.
R. Emre Erkmen - One of the best experts on this subject based on the ideXlab platform.
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Complementary Energy Based Formulation for Torsional Buckling of Columns
Journal of Engineering Mechanics, 2009Co-Authors: R. Emre Erkmen, Magdi Mohareb, M.a. BradfordAbstract:A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary Complementary Energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in Complementary Energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, Complementary Energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary Complementary Energy is considered for the elastic torsional buckling analysis of columns. The Complementary Energy expression is obtained from the well known total potential Energy functional by using Frederichs’ transformation. In contrast to flexural b...
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Buckling analysis of thin-walled open members—A Complementary Energy variational principle
Thin-Walled Structures, 2008Co-Authors: R. Emre Erkmen, Magdi MoharebAbstract:This first of two companion papers develops a new variational principle for the buckling analysis of thin-walled members based on the principle of stationary Complementary Energy. Some of the aspects of the Vlasov thin-walled beam theory (the rigid cross section assumption, and the stress expressions) are postulated to describe the behavior of members while other aspects of the theory (i.e., the zero shear strain assumption at mid-surface) are discarded. Koiter's formulation based on polar decomposition theory in finite elasticity is adopted to formulate expressions for statically admissible stress resultant fields. The stationarity conditions of the Complementary Energy expression are then evoked to yield the conditions of neutral stability and associated boundary conditions in which the rotation fields appear explicitly. The formulation seamlessly incorporates shear deformation effects and load position effects. Also, the Wagner effect and the mono-symmetry property which arise in displacement based formulations arise in the present formulation in a natural way.
Dai Xiangrong - One of the best experts on this subject based on the ideXlab platform.
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wind and light Complementary Energy storage power generation system
2014Co-Authors: Dai XiangrongAbstract:The utility model belongs to the natural Energy power generation field and relates to a wind and light Complementary Energy storage power generation system. The wind and light Complementary Energy storage power generation system includes a wind and light complementation controller, a first storage battery, an inverter and a load; the wind and light complementation controller is connected with a wind turbine and a solar panel, and includes an electrical Energy storage device; the electrical Energy storage device comprises at least a second storage battery and at least one super capacitor; the input end of the electrical Energy storage device is connected with the wind and light complementation controller; and the output end of the electrical Energy storage device is connected with the inverter. Since the wind and light Complementary Energy storage power generation system is provided with the super capacitors, the wind and light Complementary Energy storage power generation system can store a large quantity of electrical Energy, and therefore, natural Energy waste can be prevented.