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Wolfgang A Wall - One of the best experts on this subject based on the ideXlab platform.
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geometrically exact finite element formulations for slender beams kirchhoff love Theory versus simo reissner Theory
Archives of Computational Methods in Engineering, 2019Co-Authors: Christoph Meier, Alexander Popp, Wolfgang A WallAbstract:The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff–Love type, a detailed review of existing formulations of Kirchhoff–Love and Simo–Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a $$C^1$$ -continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes, preservation of objectivity and path-independence, consistent convergence orders, avoidance of locking effects as well as conservation of energy and momentum by the employed spatial discretization schemes, but also a range of practically relevant secondary aspects will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff–Love beam elements proposed in this work are the first ones of this type that fulfill all these essential requirements. On the contrary, Simo–Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff–Love formulations can provide considerable numerical advantages such as lower spatial discretization error levels, improved performance of time integration schemes as well as linear and nonlinear solvers and smooth geometry representation as compared to shear-deformable Simo–Reissner formulations when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff–Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo–Reissner element formulations from the literature.
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geometrically exact finite element formulations for curved slender beams kirchhoff love Theory vs simo reissner Theory
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Christoph Meier, Wolfgang A Wall, Alexander PoppAbstract:The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a C1-continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large-deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes or preservation of objectivity and path-independence will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff-Love beam elements proposed in this work are the first ones of this type that fulfill all the considered requirements. On the contrary, Simo-Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff-Love formulations can provide considerable numerical advantages when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff-Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo-Reissner element formulations from the literature.
Christoph Meier - One of the best experts on this subject based on the ideXlab platform.
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geometrically exact finite element formulations for slender beams kirchhoff love Theory versus simo reissner Theory
Archives of Computational Methods in Engineering, 2019Co-Authors: Christoph Meier, Alexander Popp, Wolfgang A WallAbstract:The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff–Love type, a detailed review of existing formulations of Kirchhoff–Love and Simo–Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a $$C^1$$ -continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes, preservation of objectivity and path-independence, consistent convergence orders, avoidance of locking effects as well as conservation of energy and momentum by the employed spatial discretization schemes, but also a range of practically relevant secondary aspects will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff–Love beam elements proposed in this work are the first ones of this type that fulfill all these essential requirements. On the contrary, Simo–Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff–Love formulations can provide considerable numerical advantages such as lower spatial discretization error levels, improved performance of time integration schemes as well as linear and nonlinear solvers and smooth geometry representation as compared to shear-deformable Simo–Reissner formulations when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff–Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo–Reissner element formulations from the literature.
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geometrically exact finite element formulations for curved slender beams kirchhoff love Theory vs simo reissner Theory
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Christoph Meier, Wolfgang A Wall, Alexander PoppAbstract:The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a C1-continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large-deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes or preservation of objectivity and path-independence will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff-Love beam elements proposed in this work are the first ones of this type that fulfill all the considered requirements. On the contrary, Simo-Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff-Love formulations can provide considerable numerical advantages when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff-Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo-Reissner element formulations from the literature.
Cristinel Mardare - One of the best experts on this subject based on the ideXlab platform.
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an intrinsic formulation of the kirchhoff love Theory of linearly elastic plates
Analysis and Applications, 2017Co-Authors: Philippe G Ciarlet, Cristinel MardareAbstract:We recast the displacement-traction problem of the Kirchhoff–Love Theory of linearly elastic plates as a boundary value problem with the bending moments and stress resultants inside the middle sect...
J Sladek - One of the best experts on this subject based on the ideXlab platform.
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elastodynamics of fgm plates by mesh free method
Composite Structures, 2016Co-Authors: L Sator, V Sladek, J Sladek, D L YoungAbstract:Abstract The paper deals with transient analysis of homogeneous as well as FGM (functionally graded material) thin and/or thick plates subjected to transversal dynamic loading. The Young modulus and mass density are allowed to be continuously variable through the thickness of the plate. The unified formulation is developed for plate bending problems including three various theories such as the classical Kirchhoff–Love Theory for bending of thin elastic plates, the 1st and 3rd order shear deformations plate theories. Switching among these three theories is controlled by two key factors. From the derived equations of motion, the coupling between the bending and in-plane deformation modes is discovered in FGM plates with specification of the necessary conditions. For the numerical implementation, the strong formulation is proposed with meshless approximation of spatial variations of field variables. The semi-discretized equations of motion yield a system the ordinary differential equations which can be solved by standard time stepping techniques. The great attention is paid to the numerical study of coupling effects in FGM plates subjected to transversal Heaviside impact loading and/or Heaviside pulse loading. The achieved numerical results are thoroughly discussed and interpreted.
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coupling effects in elastic analysis of fgm composite plates by mesh free methods
Composite Structures, 2014Co-Authors: L Sator, V Sladek, J SladekAbstract:Abstract In this paper we shall investigate the static response of thin and/or thick elastic functionally graded (FG) plates. The spatial variation of material coefficients in the FG composite structures is determined by distribution of volume fractions of particular constituents. The attention is devoted to derivation of the special formulation of governing equations in FGM plates, which includes the Kirchhoff–Love Theory (KLT) as well as the 1st and 3rd order shear deformation plate Theory (SDPT). The power-law gradations across the plate thickness and along in-plane coordinates yield two different problems. To facilitate the numerical solution of rather complex governing equations, we propose the strong formulation combined with Moving Least Square (MLS) approximation for field variables. Several numerical examples are presented to investigate the accuracy, convergence of accuracy and computational efficiency of studied mesh-free formulation for boundary value problems with existing benchmark solutions. The coupling effects are studied via the response of FGM square plate to static loading within the KLT as well as the 1st and 3rd order SDPT.
Alexander Popp - One of the best experts on this subject based on the ideXlab platform.
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geometrically exact finite element formulations for slender beams kirchhoff love Theory versus simo reissner Theory
Archives of Computational Methods in Engineering, 2019Co-Authors: Christoph Meier, Alexander Popp, Wolfgang A WallAbstract:The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff–Love type, a detailed review of existing formulations of Kirchhoff–Love and Simo–Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a $$C^1$$ -continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes, preservation of objectivity and path-independence, consistent convergence orders, avoidance of locking effects as well as conservation of energy and momentum by the employed spatial discretization schemes, but also a range of practically relevant secondary aspects will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff–Love beam elements proposed in this work are the first ones of this type that fulfill all these essential requirements. On the contrary, Simo–Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff–Love formulations can provide considerable numerical advantages such as lower spatial discretization error levels, improved performance of time integration schemes as well as linear and nonlinear solvers and smooth geometry representation as compared to shear-deformable Simo–Reissner formulations when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff–Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo–Reissner element formulations from the literature.
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geometrically exact finite element formulations for curved slender beams kirchhoff love Theory vs simo reissner Theory
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Christoph Meier, Wolfgang A Wall, Alexander PoppAbstract:The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a C1-continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large-deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes or preservation of objectivity and path-independence will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff-Love beam elements proposed in this work are the first ones of this type that fulfill all the considered requirements. On the contrary, Simo-Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff-Love formulations can provide considerable numerical advantages when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff-Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo-Reissner element formulations from the literature.
