Homogenization and dimensional reduction of composite plates with in-plane heterogeneity

Lee, Chang-Yong; Yu, Wenbin

doi:10.1016/j.ijsolstr.2011.01.032

Cited by 61 publications

(27 citation statements)

References 33 publications

(44 reference statements)

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“…(9) actually implies symmetry of in-plane strains, such that ε 12 = ε 21 . Based on the concept of decomposition of rotation tensor [10], the Jauman-Biot-Cauchy strain components for small local rotation are given by…”

Section: Three-dimensional Formulationmentioning

confidence: 99%

“…If we attempt to solve this problem directly, we will meet the same or even more difficulty as solving any full 3D nonlinear elasticity problem. Fortunately, as shown in [21,[34][35][36], VAM can be used to calculate the 3D unknown functions asymptotically. Although, the minimization problem can be solved analytically as shown in [34,35], the procedure becomes very tedious, even with the help of the power of present day computers and very sophisticated software packages such Mathematica TM and Matlab TM .…”

Section: Three-dimensional Formulationmentioning

confidence: 99%

“…Following [21], the VAM requires one to find the leading terms of the functional according to the different orders. For the zeroth-order approximation, these leading terms of Eq.…”

Section: Zeroth-order Approximationmentioning

confidence: 99%

“…The second example is to model a corrugated-core sandwich panel, a concept used for the Integrated Thermal Protection System (ITPS) studied in [21,29]. The ITPS panel unit cell is sketched in Fig.…”

Section: Integrated Thermal Protection Systemmentioning

confidence: 99%

“…As a remedy to the shortcomings of formal asymptotic methods, we propose to use the variational asymptotic method (VAM) [7] to carry out simultaneous homogenization and dimensional reduction, to construct a model suitable for plates made of heterogeneous materials, and to extend our previous work [21] by producing a refined model that includes transverse shear effects. First, the 3D anisotropic elasticity problem is formulated in an intrinsic form suitable for geometrically nonlinear analysis.…”

Section: Introductionmentioning

confidence: 99%

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Refined modeling of composite plates with in‐plane heterogeneity

Lee¹,

Yu²,

Hodges³

2013

Z Angew Math Mech

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This article is concerned with the mechanical behavior of heterogeneous composite plates with elastic moduli and layered geometries varying through the thickness direction and periodically along the in-plane directions. By using the concept of decomposition of the rotation tensor, we first formulate the three-dimensional elastic problem in an intrinsic form for application to the geometrically nonlinear problem. The variational asymptotic method is then exercised, leading to simultaneous homogenization and dimensional reduction to construct an effective and simple model suitable for plates with in-plane periodicity. In particular, having obtained the refinement terms up to the second order, we develop a refined plate model, namely a generalized Reissner-Mindlin model that is capable of capturing the transverse shear deformations. In order to deal with realistic and complex plate geometries and constituent materials efficiently and conveniently, the proposed model is implemented into a single unified formulation suitable for incorporation into a commercial analysis package. Numerical results computed herein for a few examples are compared to similar results available in the literature to demonstrate the application and performance of the present model.

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Section: Three-dimensional Formulationmentioning

confidence: 99%

Section: Three-dimensional Formulationmentioning

confidence: 99%

“…Following [21], the VAM requires one to find the leading terms of the functional according to the different orders. For the zeroth-order approximation, these leading terms of Eq.…”

Section: Zeroth-order Approximationmentioning

confidence: 99%

Section: Integrated Thermal Protection Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Refined modeling of composite plates with in‐plane heterogeneity

Lee¹,

Yu²,

Hodges³

2013

Z Angew Math Mech

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Numerical plate testing for linear two‐scale analyses of composite plates with in‐plane periodicity

Terada

Hirayama

Yamamoto

et al. 2015

Numerical Meth Engineering

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SUMMARYA method of numerical plate testing (NPT) for composite plates with in-plane periodic heterogeneity is proposed. In the two-scale boundary value problem, a thick plate model is employed at macroscale, while three-dimensional solids are assumed at microscale. The NPT, which is nothing more or less than the homogenization analysis, is in fact a series of microscopic analyses on a unit cell that evaluates the macroscopic plate stiffnesses. The specific functional forms of microscopic displacements are originally presented so that the relationship between the macroscopic resultant stresses/moments and strains/curvatures to be consistent with the microscopic equilibrated state. In order to perform NPT by using general-purpose FEM programs, we introduce control nodes to facilitate the multiple-point constraints for in-plane periodicity. Numerical examples are presented to verify that the proposed method of NPT reproduces the plate stiffnesses in classical plate and laminate theories. We also perform a series of homogenization, macroscopic, and localization analyses for an in-plane heterogeneous composite plate to demonstrate the performance of the proposed method.

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Analysis of the Homogenization Problem for Nonlinear Corrugated Plate

Kolpakov,

Rakin

2023

Advanced Structured Materials

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Homogenization and dimensional reduction of composite plates with in-plane heterogeneity

Cited by 61 publications

References 33 publications

Refined modeling of composite plates with in‐plane heterogeneity

Refined modeling of composite plates with in‐plane heterogeneity

Numerical plate testing for linear two‐scale analyses of composite plates with in‐plane periodicity

Analysis of the Homogenization Problem for Nonlinear Corrugated Plate

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