New structural matrices for a beam element with shear deformation

Pilkey, Walter D.; Kang, Weize; Schramm, Uwe

doi:10.1016/0168-874x(94)00055-k

Cited by 14 publications

(3 citation statements)

References 3 publications

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“…It is shown in [1,4] that the proposed solution algorithm improves the performance of CBT significantly, especially in cases where thin-walled box type cross-section are considered and torsional loading is applied. Additionally, our GBT formulation enhances the predictive quality in beam problems with unsymmetric cross-sections where Schramm et al [8,9] observed that shear elastic transverse bending load cases do not decouple based on the eigenvector of the bending stiffness tensor. Further, it can be shown that stress distributions in FGM cross-sections can be improved by our GBT formulation.…”

Section: Member Analysismentioning

confidence: 93%

On the Importance of Cross-Sectional Distortions and their Inclusion in an Efficient GBT-Formulation

Kugler¹,

Fotiu²,

Muŕın³

2021

14th WCCM-ECCOMAS Congress

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This proceeding proposes an efficient generalized beam theory formulation, which accounts for cross-sectional deformations in slender prismatic structures. It was shown by the authors in a recent publication [1] that in-plane distortional deformations and accompanied out of plane warping deformations of the cross-section influence the accuracy of results in beam dynamics especially if thin-walled cross-sections are applied. The GBT formulation proposed in [1] overcomes the inaccuracies of classical beam mechanics, however, requires a two-dimensional plane discretization of the cross-section. The computational complexity can be reduced vastly, if the thin-walled cross-sections can be discretized with one-dimensional elements. Consequently, this proceeding discusses a corresponding derivation, where the line mesh which discretizes the cross-section has six degrees of freedom at each node. The membrane part consists of mass-less micro-polar rotations (drilling rotations) and can be derived independently from the bending part, where a shear elastic formulation is selected.

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Section: Member Analysismentioning

confidence: 93%

On the Importance of Cross-Sectional Distortions and their Inclusion in an Efficient GBT-Formulation

Kugler¹,

Fotiu²,

Muŕın³

2021

14th WCCM-ECCOMAS Congress

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“…where E is the Young's modulus of elasticity; G is the shear modulus of the material;˛is a shear coefficient factor that depends on the shape of the cross-section [27], and…”

Section: Closed-form Equations Of Stiffness and Mass Matrices Of The mentioning

confidence: 99%

Dynamic analysis of the precision compliant mechanisms considering thermal effect

Zhang

Hou

2010

Precision Engineering

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“…In the formulation presented in this work, no additional terms are necessary to develop the geometric stiffness matrix since shape functions are obtained directly from the solution of the differential equations of the problem, considering the Timoshenko beam theory. Schramm et al (1994) and Pilkey et al (1995) also developed a stiffness matrix from the differential equations considering shear effects; however, shape functions were not developed.…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach to the Timoshenko Geometric Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor

Rodrigues

Burgos

Martha

2019

Lat. Am. j. solids struct.

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Nonlinear analyses using an updated Lagrangian formulation considering the Euler-Bernoulli beam theory have been developed with consistency in the literature, with different geometric matrices depending on the nonlinear displacement parts considered in the strain tensor. When performing this type of analysis using the Timoshenko beam theory, in general, the stiffness and the geometric matrices present additional degrees of freedom. This work presents a unified approach for the development of a geometric matrix employing the Timoshenko beam theory and considering higher-order terms in the strain tensor. This matrix is obtained using shape functions calculated directly from the solution of the differential equation of the problem. The matrix is implemented in the Ftool software, and its results are compared against several matrices found in the literature, with or without higher-order terms in the strain tensor, as well as the Euler-Bernoulli or Timoshenko beam theories. Examples show that the use of the Timoshenko beam theory has a strong influence, especially when the structure has small slenderness (short members). For high axial load values, the consideration of higher-order terms in the strain tensor results in larger displacements as expected.

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New structural matrices for a beam element with shear deformation

Cited by 14 publications

References 3 publications

On the Importance of Cross-Sectional Distortions and their Inclusion in an Efficient GBT-Formulation

On the Importance of Cross-Sectional Distortions and their Inclusion in an Efficient GBT-Formulation

Dynamic analysis of the precision compliant mechanisms considering thermal effect

A Unified Approach to the Timoshenko Geometric Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor

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