A higher order beam model for thin-walled structures with in-plane rigid cross-sections

Vieira, Ricardo; Virtuoso, Francisco; Pereira, E. B. R.

doi:10.1016/j.engstruct.2014.11.008

Cited by 20 publications

(3 citation statements)

References 49 publications

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“…At present, GBT has been used to perform first-order [27], buckling [28], post buckling [29], vibration [30] and dynamic analyses [31] of thin-walled structures. Besides, Vieira et al [32] have also developed a higher order theory, which initially considers the displacement field through the interpolation over the meshed cross-section [33]. Towards an efficient application, a criterion is developed to uncouple the governing equations by solving the associated polynomial eigenvalue problem [34].…”

Section: Introductionmentioning

confidence: 99%

Application of Pattern Recognition to the Identification of Cross-Section Deformation Modes of Thin-Walled Structures

Zhang

Zhu

2019

IEEE Access

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This paper presents a novel procedure to identify cross-section deformation modes of thin-walled structures with the application of pattern recognition. Initially, a higher order model is derived by considering an approximation of cross-section deformation by a set of basis functions, which are integrated in the governing equations and decoupled through the solution of the associated generalized eigenvalue problem. The eigenvectors obtained are deemed to inherit the attributes of structural behaviors, and thus can serve as the basis to identify deformation modes. Accordingly, these eigenvectors are further handled employing the singular value decomposition, in order to recognize the axial variation patterns of the basis functions. Next, each eigenvector is orthogonally decomposed into components corresponding to the variation patterns, with their proportional relationship, which is really pursued, being obtained and used as the weights to ''assemble'' basis functions to generate deformation modes. Moreover, a numbering system is proposed to hierarchically organize these deformation modes. Finally, a reduced higher order model can be obtained by updating the initial governing equations with a selective set of cross-section deformation modes. The main features lie in the capability to be numerically implemented in a simple and intuitive way and the nature to give identified deformation modes mechanical interpretation inherited from actual dynamic behaviors of thin-walled structures. The versatility of the procedure as well as the resulting beam model has been validated through both numerical examples and comparisons with other theories. INDEX TERMS Thin-walled structures, cross-section deformation modes, pattern recognition, a higher order beam theory.

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Section: Introductionmentioning

confidence: 99%

Application of Pattern Recognition to the Identification of Cross-Section Deformation Modes of Thin-Walled Structures

Zhang

Zhu

2019

IEEE Access

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“…At present, GBT has been well-established as an efficient and versatile tool to perform first-order [26], buckling [27], vibration [28], post buckling [29] and dynamic analyses [30] of thin-walled structures in elasticity. Another procedure to define deformation modes was proposed by Vieira et al [31]. It considers an enrichment of the displacement field on the cross-section through a set of interpolation functions defined over a mesh of the cross-section, and a set of uncoupled deformation modes representing higher order effects are derived based on the solution of a polynomial eigenvalue problem [32,33].…”

Section: Introductionmentioning

confidence: 99%

A Novel Approach to Perform the Identification of Cross-Section Deformation Modes for Thin-Walled Structures in the Framework of a Higher Order Beam Theory

Zhang

Zhu

2019

Applied Sciences

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This paper presents a novel approach to identify cross-section deformation modes for thin-walled structures by assembling preliminary deformation modes (PDM) considering their participation in free vibration modes. These PDM, defined over the cross-section through kinematic concepts, are integrated in the governing equations of a higher order model and then uncoupled in the form of generalized eigenvectors. The eigenvectors are deemed to inherit the attributes of structural behaviours and can serve as the basis to assemble PDM. Accordingly, a criterion was developed to handle the eigenvectors, pursuing (i) the clustering of PDM that participate in a same structural behaviour, (ii) the assignation of the corresponding weights that indicate their participation and (iii) the decomposition of an amplitude function when it is related to several structural behaviours. Moreover, a numbering system was proposed to hierarchically organize the deformation modes, which is conducive to a reduced higher order model. The main features of this approach are found in its ability to be performed in a more operational way and its nature to give deformation modes physical interpretation inherited from the dynamic behaviours. The versatility of the approach was validated through both numerical examples and comparisons with other theories.

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“…Based on the boundary element method, Sapountzakis and Tsipiras [39] and Sapountzakis and Dourakopoulos [40] introduced a beam model for torsion and compression analysis of beams with arbitrary cross-section and encompassing various higher-order effects. Vieira et al [41] discussed the geometrically nonlinear analysis of thin-walled structures be employing an higher-order beam model which utilizes the integration over the cross-section of the elasticity equations, appropriately weighted by in-plane approximation functions. Recently, Garcea et al [42] addressed the geometrically nonlinear analysis of beams and shells using solid finite elements and highlighted the advantages of mixed stress/displacement formulations when applied to the path-following analysis and Koiter asymptotic method.…”

Section: Introductionmentioning

confidence: 99%

Unified formulation of geometrically nonlinear refined beam theories

Pagani

Carrera

2016

Mechanics of Advanced Materials and Structures

135

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By using the Carrera Unified Formulation (CUF) and a total Lagrangian approach, the unified theory of beams including geometrical nonlinearities is introduced in this paper. According to CUF, kinematics of one-dimensional structures are formulated by employing an index notation and a generalized expansion of the primary variables by arbitrary cross-section functions. Namely, in this work, low-to higher-order beam models with only pure displacement variables are implemented by utilizing Lagrange polynomials expansions of the unknowns on the cross-section. The principle of virtual work and a finite element approximation are used to formulate the governing equations, whereas a Newton-Raphson linearization scheme along with a path-following method based on the arc-length constraint is employed to solve the geometrically nonlinear problem. By using CUF and three-dimensional Green-Lagrange strain components, the explicit forms of the secant and tangent stiffness matrices of the unified beam element are provided in terms of fundamental nuclei, which are invariants of the theory approximation order. A symmetric form of the secant matrix is provided as well by exploiting the linearization of the geometric stiffness terms. Various numerical assessments are proposed, including large deflection analysis, buckling and post-buckling of slender solid cross-section beams. Thin-walled structures are also analysed in order to show the enhanced capabilities of the present formulation. Whenever possible, the results are compared to those from the literature and finite element commercial software tools.

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A higher order beam model for thin-walled structures with in-plane rigid cross-sections

Cited by 20 publications

References 49 publications

Application of Pattern Recognition to the Identification of Cross-Section Deformation Modes of Thin-Walled Structures

Application of Pattern Recognition to the Identification of Cross-Section Deformation Modes of Thin-Walled Structures

A Novel Approach to Perform the Identification of Cross-Section Deformation Modes for Thin-Walled Structures in the Framework of a Higher Order Beam Theory

Unified formulation of geometrically nonlinear refined beam theories

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