Asymptotic construction of Reissner-like composite plate theory with accurate strain recovery

Yu, Wenbin; Hodges, Dewey H.; Volovoi, Vitali

doi:10.1016/s0020-7683(02)00410-9

Cited by 114 publications

(69 citation statements)

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“…Another way to avoid the problem associated with boundary conditions is to derive a Reissner-Mindlin-like (RM-like) plate theory. Recently, Yu et al [2002] and Yu [2005] have developed the RM-like plate models by applying the VAM and using the through-thethickness finite element analysis. These models are not claimed to be asymptotically correct.…”

Section: Introductionmentioning

confidence: 99%

An asymptotic analysis of anisotropic heterogeneous plates with consideration of end effects

Kim

2010

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A finite element-based asymptotic analysis tool is developed for general anisotropic plates. The formulation begins with three-dimensional equilibrium equations in which the thickness coordinate is scaled by the characteristic length of the plate. This allows us to split the equations into two parts, such as the one-dimensional microscopic equations and the two-dimensional macroscopic equations, via the virtual work concept. The one-dimensional microscopic analysis yields the through-the-thickness warping function at each level, which does not require two-dimensional macroscopic analysis. The two-dimensional macroscopic equations provide the governing equations of the plate at each level in a recursive form. These can be solved in an orderly manner, in which proper macroscopic boundary conditions should be incorporated. The displacement prescribed boundary condition is obtained by introducing the orthogonality condition of asymptotic displacements to the plate fundamental solutions. In this way, the end effects of the plate are kinematically corrected without applying the sophisticated decay analysis method. The developed asymptotic analysis method is applied to semiinfinite plates with simply supported and clamped-free boundary conditions. The results obtained are compared to those of three-dimensional FEM, three-dimensional elasticity, and Reissner-Mindlin plate theory. The usefulness of the present method is also discussed.

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Section: Introductionmentioning

confidence: 99%

An asymptotic analysis of anisotropic heterogeneous plates with consideration of end effects

Kim

2010

JOMMS

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“…The through-the-thickness analysis produces the 2-D constitutive law and non-mechanical stress resultants to be used in the 2-D plate analysis, along with recovering relations that yield the 3-D displacement, strain and stress fields through the thickness using results obtained from the solution of the 2-D problem. The present work extends a simple yet accurate model developed recently for composite plates and shells, namely \'ariational Asymptotic Plate and Shell Analysis (VAPAS) by Yu et al (2002aYu et al ( ,b, 2003 so that thermoelastic effects can be treated in the same framework.Since the procedure is quite similar, the authors have chosen to repeat some formulae and text from their previous publications in order to make the present paper more selfcontained. The present theory has been implemented into the computer program VAPAS.…”

mentioning

confidence: 74%

“…If we attempt to solve this problem directly, we will meet the same difficulty as solving any full 3-D elasticity problem. Fortunately, as shown in Yu et al (2002aYu et al ( ,b, 2003, the VAM can be used to calculate the 3-D warping functions asymptotically. The throughthe-thickness analysis is one dimensional and can be solved analj1;ically.…”

Section: Of 39mentioning

confidence: 96%

Section: Of 39mentioning

confidence: 99%

“…These matrices are in general fully populated. However, if it is desired to model laminated composite plates in which each lamina exhibits a monocUnic sjonmetry about its own mid-plane and is rotated about the local normal to be a layer in the composite laminated plate, then as shown in Yu et al (2002a), some parts of these matrices will always vanish no matter what the layup angle is.To deal with applied mechanical loads as well with thermal loads, we will at first leave open the existence of a potential energy and develop instead the virtual work of the applied mechanical loads. The virtual displacement is taken as the Lagrangean variation of the 6 OF 39 displacement field, such that…”

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confidence: 99%

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Multi-Body Approach to the Dynamic Analysis of Space Structures with Actuated Components

Bauchau¹

2001

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The bubllc reporting burden for this collection of Information Is estimated to average 1 hour per response, including the tim^ gathering end maintaining the data needed, and completing and reviewing the collection of information. Send comments regan of irifCrmation, Including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Si (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that A. subject to any penalty for failing to comply with a collection of information If it does not display a currently valid 0MB control numoBr. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DP-MM-YYYY) 2. REPORT TYPE Final Report DATES COVERED (From -To)Dec 15, 00 -Dec 14, 03 TITLE AND SUBTITLEMxUtibody Approach to the Dynamic Analusis of Structures with ActuatedComponents 5a. CONTRACT NUMBER 5b. GRANT NUMBER F49620-01-1-0038 5c. PROGRAM ELEMENT NUMBER AUTHOR(S)Dr. Oliver A. Bauchau 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)Gerogia Tech Research Corporation Gerogia Institute of Technology Atlanta, GA 30332-0420 PERFORMING ORGANIZATION REPORT NUMBER SPONSORING/MONITORING AGENCY NAME{S) AND ADDRESS(ES) Department of the Air Force 4015 Wilson Blvd. Air Force Office of Scientific ResearchArlington, VA 22203-1954 High-fidelity, finite-element-based dimensionally reduced models have been constructed for composite plates and shells, including hygrothermal and piezoelectric effects, \mder the sponsorship of AFOSR. In these models, the smallness of the thickness has beea used to advantage to rigorously reduce the original three-dimensional geometrically nonlinear elasticity theory to two-dimensional Reissner-Mindlin type theory for plates and shells. The resulting theory can achieve an accuracy comparable to higher-order layerwise theories at the cost of only a first-order shear deformation theory. The dimensional reduction process and the recovery relations for the original three-dimensional displacements/strains/stresses are implemented in a finite-element code, Variational Asyinptotic Plate and Shell Analysis (VAPAS). This program is connected with DYMORE, a nonlinear finite-elemfent based multi-body dynamic code to provide an efficient and accurate simulation capability for space systems involving composite and inflatable components with actuated elements which are required for current and fiiture Air Force missions. SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S)12 SUBJECT TERMS SECURITY CLASSIFICATION OF: a. REPORT b. ABSTRACT c. THIS PAGE LIMITATION OF ABSTRACT NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSONDr. Oliver A. Bauchau 19b. TELEPHONE NUMBER (Include area code) 404-894-4763Standard Form 298 (Rev. 8/98)Prescribed by ANSI Std. Z39.18 IntroductionThis three-year grant was initiated in December 2000. All work done under the auspices of the grant is sxunmarized herein, and the various papers written under grant sponsorship are appended to pro...

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2015

Homogenization of Heterogeneous Thin and Thick Plates

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Asymptotic construction of Reissner-like composite plate theory with accurate strain recovery

Cited by 114 publications

References 12 publications

An asymptotic analysis of anisotropic heterogeneous plates with consideration of end effects

An asymptotic analysis of anisotropic heterogeneous plates with consideration of end effects

Multi-Body Approach to the Dynamic Analysis of Space Structures with Actuated Components

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