The Finite Element Analysis of Shells - Fundamentals

Chapelle, Dominique; Bathe, Klaus-Jrgen

doi:10.1007/978-3-642-16408-8

Cited by 185 publications

(316 citation statements)

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“…We wish to truncate the Taylor series approximation for u such that the resulting shell model is asymptotically consistent with three-dimensional solid mechanics [15]; thereby allowing for the use of fully three-dimensional constitutive equations in the mathematical model and subsequent numerical implementation. We therefore restrict the displacement field to the following seven-parameter expansion 160 V. P. Vallala and J. N. Reddy…”

Section: Assumed 7-parameter Displacement Fieldmentioning

confidence: 99%

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

Vallala

Reddy

2013

MCA

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Abstract-This study deals with the use of high-order spectral/hp approximation functions in finite element models of various of nonlinear boundary-value and initial-value problems arising in the fields of structural mechanics and flows of viscous incompressible fluids. For many of these classes of problems, the high-order (typically, polynomial order 4  p ) spectral/hp finite element technology offers many computational advantages over traditional low-order (i.e., 3 < p ) finite elements. For instance, higher-order spectral/hp finite element procedures allow us to develop robust structural elements such as beams, plates, and shells in a purely displacement-based setting, which avoid all forms of numerical locking. For fluid flows, when combined with least-squares variational principles, the higher-order spectral/hp technology allows us to develop efficient finite element models that always yield a symmetric positive-definite (SPD) coefficient matrix and, hence, robust iterative solvers can be used. Also, the use of spectral/hp finite element technology results in a better conservation of physical quantities like dilatation, volume, and mass, and stable evolution of variables with time for transient flows. The present study considers the weak-form based displacement finite element models elastic shells and the least-squares finite element models of the Navier-Stokes equations governing flows of viscous incompressible fluids. Numerical solutions of several nontrivial benchmark problems are presented to illustrate the accuracy and robustness of the developed finite element technology.

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Section: Assumed 7-parameter Displacement Fieldmentioning

confidence: 99%

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

Vallala

Reddy

2013

MCA

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“…The study of the transition from periodic to chaotic vibrations is of primary interest in numerous applied fields such as aeronautic and aerospace or civil engineering, where shell-like structural components are often used [1,2]. Another field where chaotic vibration of shells is searched for, is that of musical acoustics and more precisely the sound of gongs and cymbals where the chaotic nature of the vibration ensures for the peculiar bright and shimmering sound of these instruments [3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates

Touzé

Thomas

Amabili

2011

International Journal of Non-Linear Mechanics

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The transition from periodic to chaotic vibrations in free-edge, perfect and imperfect circular plates, is numerically studied. A pointwise harmonic forcing with constant frequency and increasing amplitude is applied to observe the bifurcation scenario. The von Kármán equations for thin plates, including geometric nonlinearity, are used to model the large amplitude vibrations. A Galerkin approach based on the eigenmodes of the perfect plate allows discretizing the structure. The resulting ordinary-differential equations are numerically integrated. Bifurcation diagrams of Poincaré maps, Lyapunov exponents and Fourier spectra analysis reveals the transitions and the energy exchange between modes. The transition to chaotic vibration is studied in the frequency range of the first eigenfrequencies. The complete bifurcation diagram and the critical forces needed to attain the chaotic regime are especially adressed. For perfect plates, it is found that a direct transition from periodic to chaotic vibrations is at hand. For imperfect plates displaying specific internal resonance relationships, the energy is first exchanged between resonant modes before the chaotic regime. Finally, the nature of the chaotic regime, where a high-dimensional chaos is numerically found, is questioned within the framework of wave turbulence. These numerical findings confirm a number of experimental observations made on shells, where the generic route to chaos displays a quasiperiodic regime before the chaotic state, where the modes, sharing internal resonance relationship with the excitation frequency, ap- *

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“…The nonlinear structural problem is discretized by means of MITC4 shell elements [20,21], where the typical constraints of Reissner-Mindlin shell kinematics are enforced.…”

Section: Shell Structural Solvermentioning

confidence: 99%

An explicit dynamics GPU structural solver for thin shell finite elements

Bartezzaghi

Cremonesi

Parolini

et al. 2015

Computers & Structures

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With the availability of user oriented software tools, dedicated architectures, such as the parallel computing platform and programming model CUDA (Compute Unified Device Architecture) released by NVIDIA, one of the main producers of graphics cards, and of improved, highly performing GPU (Graphics Processing Unit) boards, GPGPU (General Purpose programming on GPU) is attracting increasing interest in the engineering community, for the development of analysis tools suitable to be used in validation/verification and virtual reality applications. For their inherent explicit and decoupled structure, explicit dynamics finite element formulations appear to be particularly attractive for implementations on hybrid CPU/GPU or pure GPU architectures. The issue of an optimized, double-precision finite element GPU implementation of an explicit dynamics finite element solver for elastic shell problems in small strains and large displacements and rotations, using unstructured meshes, is here addressed. The conceptual difference between a GPU implementation directly adapted from a standard CPU approach and a new optimized formulation, specifically conceived for GPUs, is discussed and comparatively assessed. It is shown that a speedup factor of about 5 can be achieved by an optimized algorithm reformulation and careful memory management. A speedup of more than 40 is achieved with respect of state-of-the art commercial codes running on CPU, obtaining real-time simulations in some cases, on commodity hardware. When a last generation GPU board is used, it is shown that a problem with more than 16 millions degrees of freedom can be solved in just few hours of computing time, opening the way to virtualization approaches for real large scale engineering problems.

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The Finite Element Analysis of Shells - Fundamentals

Cited by 185 publications

References 0 publications

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates

An explicit dynamics GPU structural solver for thin shell finite elements

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