Computer Analysis of Cylindrical Shells

Scordelis, Alexander C.; Lo, K. S.

doi:10.14359/7796

Cited by 36 publications

(7 citation statements)

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“…in much of the related literature is perhaps the most common suite of problems where converged pointwise values are used to indicate validity [72,37]. Unfortunately, these values only agree up to a few digits of precision and are therefore not reliable for a rigorous assessment of convergence.…”

Section: Numerical Resultsmentioning

confidence: 99%

Weak Boundary Condition Enforcement for Linear Kirchhoff-Love Shells: Formulation, Error Analysis, and Verification

Benzaken,

Evans,

McCormick

et al. 2020

Preprint

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Stable and accurate modeling of thin shells requires proper enforcement of all types of boundary conditions. Unfortunately, for Kirchhoff-Love shells, strong enforcement of Dirichlet boundary conditions is difficult because both functional and derivative boundary conditions must be applied. A popular alternative is to employ Nitsche's method to weakly enforce all boundary conditions. However, while many Nitsche-based formulations have been proposed in the literature, they lack comprehensive error analyses and verifications. In fact, existing formulations are variationally inconsistent and yield sub-optimal convergence rates when used with common boundary condition specifications. In this paper, we present a novel Nitsche-based formulation for the linear Kirchhoff-Love shell that is provably stable and optimally convergent for general sets of admissible boundary conditions. To arrive at our formulation, we first present a framework for constructing Nitsche's method for any abstract variational constrained minimization problem. We then apply this framework to the linear Kirchhoff-Love shell and, for the particular case of NURBS-based isogeometric analysis, we prove that the resulting formulation yields optimal convergence rates in both the shell energy norm and the standard L 2 -norm. To arrive at this formulation, we derive the Euler-Lagrange equations for general sets of admissible boundary conditions and show that the Euler-Lagrange boundary conditions typically presented in the literature is incorrect. We verify our formulation by manufacturing solutions for a new shell obstacle course that encompasses flat, parabolic, hyperbolic, and elliptic geometric configurations with a variety of common boundary condition specifications. These manufactured solutions allow us to robustly measure the error across the entire shell in contrast with current best practices where displacement and stress errors are only measured at specific locations. We use NURBS discretizations to represent the shell geometry and show optimal convergence rates in both the shell energy norm and the standard L 2 -norm with varying polynomial degrees for all of the problems in the obstacle course.

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Section: Numerical Resultsmentioning

confidence: 99%

Weak Boundary Condition Enforcement for Linear Kirchhoff-Love Shells: Formulation, Error Analysis, and Verification

Benzaken,

Evans,

McCormick

et al. 2020

Preprint

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“…The vertical displacement of the midpoint of the side edge is measured as the vertical deflection of the shell to evaluate the accuracy and convergence of the system. It is first normalized by the reference value 0.3024 m suggested by Scordelis et al [40] before plotted in Fig. 14.…”

Section: Elastic Case 2: Scordelis-lo Roofmentioning

confidence: 99%

Peridynamic Modeling of Brittle Fracture in Mindlin-Reissner Shell Theory

Li¹,

Lai²,

Liu³

2022

Computer Modeling in Engineering &Amp; Sciences

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In this work, we modeled the brittle fracture of shell structure in the framework of Peridynamics Mindlin-Reissener shell theory, in which the shell is described by material points in the mean-plane with its drilling rotation neglected in kinematic assumption. To improve the numerical accuracy, the stress-point method is utilized to eliminate the numerical instability induced by the zero-energy mode and rank-deficiency. The crack surface is represented explicitly by stress points, and a novel general crack criterion is proposed based on that. Instead of the critical stretch used in common peridynamic solid, it is convenient to describe the material failure by using the classic constitutive model in continuum mechanics. In this work, a concise crack simulation algorithm is also provided to describe the crack path and its development, in order to simulate the brittle fracture of the shell structure. Numerical examples are presented to validate and demonstrate our proposed model. Results reveal that our model has good accuracy and capability to represent crack propagation and branch spontaneously.

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“…The Scordelis-Lo roof problem [47] is considered a benchmark test for solid [37], shell [7,9,43] and solidshell FE [22,23] formulations investigating the ability of an element to model complex states of membrane strain [9]. The problem consists in the loading under vertical pressure of a single curvature thin shell supported by rigid diaphragms in the two curved edges, while keeping free the straight ones.…”

Section: "Scordelis-lo" Roofmentioning

confidence: 99%

Accurate and locking-free analysis of beams, plates and shells using solid elements

et al. 2021

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This paper investigates the capacity of solid finite elements with independent interpolations for displacements and strains to address shear, membrane and volumetric locking in the analysis of beam, plate and shell structures. The performance of the proposed strain/displacement formulation is compared to the standard one through a set of eleven benchmark problems. In addition to the relative performance of both finite element formulations, the paper studies the effect of discretization and material characteristics. The first refers to different solid element typologies (hexahedra, prisms) and shapes (regular, skewed, warped configurations). The second refers to isotropic, orthotropic and layered materials, and nearly incompressible states. For the analysis of nearly incompressible cases, the B-bar method is employed in both standard and strain/displacement formulations. Numerical results show the enhanced accuracy of the proposed strain/displacement formulation in predicting stresses and displacements, as well as producing locking-free discrete solutions, which converge asymptotically to the corresponding continuous problems.

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Computer Analysis of Cylindrical Shells

Cited by 36 publications

References 0 publications

Weak Boundary Condition Enforcement for Linear Kirchhoff-Love Shells: Formulation, Error Analysis, and Verification

Weak Boundary Condition Enforcement for Linear Kirchhoff-Love Shells: Formulation, Error Analysis, and Verification

Peridynamic Modeling of Brittle Fracture in Mindlin-Reissner Shell Theory

Accurate and locking-free analysis of beams, plates and shells using solid elements

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