Geometrically nonlinear refined shell theories by Carrera Unified Formulation

Wu, Bin; Pagani, Alfonso; Chen, W. Q.; Carrera, Erasmo

doi:10.1080/15376494.2019.1702237

Cited by 74 publications

(36 citation statements)

References 53 publications

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“…1. For the sake of brevity, the complete description of the shell formulation is not the purpose of this work, and interested readers are referred to [10,21,47].…”

Section: Preliminariesmentioning

confidence: 99%

“…where b l and b nl are the linear and nonlinear differential operators, and u is the 3D displacement vector. These differential operators in the case of 2D model are reported in [2,21]. The displacement vector is defined as…”

Section: Preliminariesmentioning

confidence: 99%

“…Considering the TL formulation and introducing the geometrical and constitutive relations, the virtual variation of the internal strain energy is formulated as (omitting some mathematical steps, which can be found in [21])…”

Section: Nonlinear Governing Equationsmentioning

confidence: 99%

“…is the secant stiffness matrix. For the sake of brevity, the complete form of this matrix is omitted, see [21]. The virtual variation of the external work can be written as…”

Section: Nonlinear Governing Equationsmentioning

confidence: 99%

“…As reported by Pagani et al [20], these structures are prone to support large displacements and rotations, and snapping phenomena can occur. Consequently, Wu et al [21] described that an accurate failure prediction is of primary importance in the analyses of the nonlinear response of highly flexible structures in the geometrical nonlinear domain. In the open literature, there are several studies related to higher-order shell models in order to accurately perform geometrical nonlinear analyses.…”

Section: Introductionmentioning

confidence: 99%

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Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

et al. 2020

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The present paper presents the evaluation of three-dimensional (3D) stress distributions of shell structures in the large displacement and rotation fields. The proposed geometrical nonlinear model is based on a combination of the Carrera Unified Formulation (CUF) and the Finite Element Method (FEM). Besides, a Newton-Raphson linearization scheme is adopted to compute the geometrical nonlinear equations, which are constrained using the arc-length path-following method. Static analyses are performed using refined models and the full Green-Lagrange strain-displacement relations. The Second Piola-Kirchhoff (PK2) stress distributions are evaluated, and lower- to higher-order expansions are employed. Popular benchmarks problems are analyzed, including cylindrical isotropic shell structure with various boundary and loading conditions. Various numerical assessments for different equilibrium conditions in the moderate and large displacement fields are proposed. Results show the distribution of axial and shear stresses, varying the refinement of the proposed two-dimensional (2D) shell model. It is shown that for axial components, a lower-order expansion is sufficient, whereas a higher-order one is needed to accurately predict shear stresses.

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“…1. For the sake of brevity, the complete description of the shell formulation is not the purpose of this work, and interested readers are referred to [10,21,47].…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Nonlinear Governing Equationsmentioning

confidence: 99%

“…is the secant stiffness matrix. For the sake of brevity, the complete form of this matrix is omitted, see [21]. The virtual variation of the external work can be written as…”

Section: Nonlinear Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

et al. 2020

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A high‐order shell finite element for the large deformation analysis of soft material structures

Pagani,

Augello,

Carrera

2024

Numerical Meth Engineering

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SummaryThis work proposes a higher‐order unified shell finite element for the analysis of cylinders made of compressible and nearly incompressible hyperelastic materials. The nonlinear governing equations are derived employing the Carrera unified formulation (CUF), thanks to which it is possible to build shell elements with the capability to capture three‐dimensional (3D) transverse and out‐of‐plane effects. The material and geometric nonlinearities are expressed in an orthogonal curvilinear reference system and the coupled formulation of hyperelastic constitutive law is considered. The principle of virtual work and a total Lagrangian approach is used to derive the nonlinear governing equations, which are solved by a Newton–Raphson scheme. The numerical investigations deal with a curved arch and both thick and thin cylinders subjected to line and point loadings. The obtained results are validated by comparing them with those from the literature. They demonstrate the reliability of the proposed method to analyze compressible and incompressible hyperelastic shell structures.

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Large deflection of composite beams by finite elements with node-dependent kinematics

2022

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In this paper, the use of the node-dependent kinematics concept for the geometrical nonlinear analysis of composite one-dimensional structures is proposed With the present approach, the kinematics can be independent in each element node. Therefore the theory of structures changes continuously over the structural domain, describing remarkable cross-section deformation with higher-order kinematics and giving a lower-order kinematic to those portion of the structure which does not require a refinement. In this way, the reliability of the simulation is ensured, keeping a reasonable computational cost. This is possible by Carrera unified formulation, which allows writing finite element nonlinear equilibrium and incremental equations in compact and recursive form. Compact and thin-walled composite structures are analyzed, with symmetric and unsymmetric loading conditions, to test the present approach when dealing with warping and torsion phenomena. Results show how finite element models with node-dependent behave as well as ones with uniform highly refined kinematic. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by node-dependent kinematics analysis.

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Geometrically nonlinear refined shell theories by Carrera Unified Formulation

Cited by 74 publications

References 53 publications

Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

A high‐order shell finite element for the large deformation analysis of soft material structures

Large deflection of composite beams by finite elements with node-dependent kinematics

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