A global-local approach for the elastoplastic analysis of compact and thin-walled structures via refined models

Petrolo, Marco; Nagaraj, Manish; Kaleel, Ibrahim; Carrera, Erasmo

doi:10.1016/j.compstruc.2018.06.004

Cited by 31 publications

(13 citation statements)

References 19 publications

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“…Previous research based on the state-of-the-art Unified Formulation [33][34][35][36][37][38][39][40][41][42][43][44][45][46] has highlighted its ability in solving a wide range of structural mechanics problems in a computationally efficient manner. However, its modelling capabilities were limited to prismatic structures.…”

Section: Discussionmentioning

confidence: 99%

“…As a result, only prismatic structures can be modelled. This procedure of evaluating the Jacobian matrix is followed in all the research published using the Unified Formulation [33][34][35][36][37][38][39][40][41][42][43][44][45][46], where 2D and 1D integrals-over the crosssection and along the beam-are performed separately by employing 2D and 1D Jacobians given by…”

Section: Beam Elementmentioning

confidence: 99%

“…As such, the method is able to recover 3D displacement and stress/strain fields in a computationally efficient manner. In recent years, several research papers have been published on the Unified Formulation framework to study linear and nonlinear deflections [33][34][35][36], 3D stress fields [37][38][39][40], failure and damage mechanics [41,42], free vibrations [43,44], buckling, and post-buckling behaviour [45,46], of both metallic and composite structures. However, the existing modelling capabilities are largely limited to prismatic structures and, therefore, are not immediately suited for analysing complex, real-life, geometrical configurations.…”

Section: Introductionmentioning

confidence: 99%

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Efficient modelling of beam-like structures with general non-prismatic, curved geometry

Patni

Minera

Pirrera

2020

Computers & Structures

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The analysis of three-dimensional (3D) stress states can be complex and computationally expensive, especially when large deflections cause a nonlinear structural response. Slender structures are conventionally modelled as one-dimensional beams but even these rather simpler analyses can become complicated, e.g. for variable cross-sections and planforms (i.e. non-prismatic curved beams). In this paper, we present an alternative procedure based on the recently developed Unified Formulation in which the kinematic description of a beam builds upon two shape functions, one for the beam's axis, the other for its cross-section. This approach predicts 3D displacement and stress fields accurately and is computationally efficient in comparison with 3D finite elements. However, current modelling capabilities are limited to the use of prismatic elements. As a means for further applicability, we propose a method to create beam elements with variable planform and variable cross-section, i.e. of general shape. This method employs an additional set of shape functions which describes the geometry of the structure exactly. These functions are different from those used for describing the kinematics and provide local curvilinear basis vectors upon which 3D Jacobian transformation matrices are produced to define non-prismatic elements. The model proposed is benchmarked against 3D finite element analyses, as well as analytical and experimental results available in the literature. Significant computational efficiency gains over 3D finite elements are observed for similar levels of accuracy, for both linear and geometrically nonlinear analyses.

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Section: Discussionmentioning

confidence: 99%

Section: Beam Elementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient modelling of beam-like structures with general non-prismatic, curved geometry

Patni

Minera

Pirrera

2020

Computers & Structures

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“…In the present paper, the Carrera Unified Formulation (CUF), which has been proved to be an efficient and accurate method for solving nonlinear structural problems [34,35,36,37,38,39,40], is now extended to deal with geometrically nonlinear analysis of composite plates. In this work, the layerwise (LW) approach based on Lagrange expansions is employed (see [41,42] for an exhaustive derivation of CUF in LW framework).…”

Section: Introductionmentioning

confidence: 99%

Buckling and post-buckling of anisotropic flat panels subjected to axial and shear in-plane loadings accounting for classical and refined structural and nonlinear theories

Carrera

Azzara²,

Daneshkhah³

et al. 2021

International Journal of Non-Linear Mechanics

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This article investigates the large deflection and post-buckling of composite plates by employing the Carrera Unified Formulation (CUF). As a consequence, the geometrically nonlinear governing equations and the relevant incremental equations are derived in terms of fundamental nuclei, which are invariant of the theory approximation order. By using the Lagrange expansion functions across the laminate thickness and the classical finite element (FE) approximation, layerwise (LW) refined plate models are implemented. The Newton-Raphson linearization scheme with the path-following method based on the arc-length constraint is employed to solve geometrically nonlinear composite plate problems. In this study, different composite plates subjected to large deflections/rotations and post-buckling are analyzed, and the corresponding equilibrium curves are compared with the results in the available literature or the traditional FEM-based solutions. The effects of various parameters, such as stacking sequence, number of layers, loading conditions, and edge conditions are demonstrated. The accuracy and reliability of the proposed method for solving the composite plates' geometrically nonlinear problems are verified.

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“…For the simplicity and the ease of applying optimization algorithms coupled with computational efficiency, one-dimensional theories are more preferred than two-and three-dimensional models. However, the development of an efficient onedimensional theory faces a fundamental challenge: a general and easy-to-implement procedure to identify the cross-section modes [1]. Ideally, this procedure should lead to a hierarchical set of modes, in the sense that only the first few modes should be sufficient to describe the deformed configuration with an "acceptable precision" [2].…”

Section: Introductionmentioning

confidence: 99%

A new approach to the identification of distortion modes of thin-walled structures based on plate/shell theory

Zhang

Zhu

et al. 2019

MATEC Web Conf.

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In this paper, a new approach to identify cross-section deformation modes is presented and utilized in the establishment of a high-order beam model for dynamic analyses of thin-walled structures. Towards this end, a systematic procedure to extract cross-section in-plane vibration shapes for a thin-walled cross-section is developed based on elastic plate/shell theory. Then the distortion shapes are separated from vibration shapes by removing the components of classic modes involved with the minimum value problem of 2-norm. Sequentially, curve fitting method is utilized to approximate the distortion shape functions along the cross-section midline. It should be noticed that these distortion modes are arranged in hierarchy consistent with the order that they are identified and the number of distortions to be identified depends on the required model precision. Based on this, Hamilton's principle is applied to formulate the dynamic governing equations of the beam by constructing its displacement field with the linear superposition of the cross-section mode shapes including distortions. Numerical examples are also presented to validate the new approach and to demonstrate its efficiency in the reproduction of three-dimensional behaviours of thin-walled structures in dynamic analyses.

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A global-local approach for the elastoplastic analysis of compact and thin-walled structures via refined models

Cited by 31 publications

References 19 publications

Efficient modelling of beam-like structures with general non-prismatic, curved geometry

Efficient modelling of beam-like structures with general non-prismatic, curved geometry

Buckling and post-buckling of anisotropic flat panels subjected to axial and shear in-plane loadings accounting for classical and refined structural and nonlinear theories

A new approach to the identification of distortion modes of thin-walled structures based on plate/shell theory

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