A Variational-Asymptotic Cell Method for Periodically Heterogeneous Materials

Materials ◽  
2005 ◽  
Author(s):  
Wenbin Yu
Keyword(s):  
Asymptotic Method ◽  
Material Properties ◽  
Ad Hoc ◽  
Asymptotic Methods ◽  
Closed Form Solution ◽  
Form Solution ◽  
Homogenization Theory ◽  
Cell Method ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method

A new cell method, variational-asymptotic cell method (VACM), is developed to homogenize periodically heterogenous anisotropic materials based on the variational asymptotic method. The variational asymptotic method is a mathematical technique to synthesize both merits of variational methods and asymptotic methods by carrying out the asymptotic expansion of the functional governing the physical problem. Taking advantage of the small parameter (the periodicity in this case) inherent in the heterogenous solids, we can use the variational asymptotic method to systematically obtain the effective material properties. The main advantages of VACM are that: a) it does not rely on ad hoc assumptions; b) it has the same rigor as mathematical homogenization theories; c) its numerical implementation is straightforward because of its variational nature; d) it can calculate different material properties in different directions simultaneously without multiple analyses. To illustrate the application of VACM, a binary composite with two orthotropic layers are studied analytically, and a closed-form solution is given for effective stiffness matrix and the corresponding effective engineering constants. It is shown that VACM can reproduce the results of a mathematical homogenization theory.

scholarly journals Cross-Layer Routing for Outage Minimization in Multihop Ad-Hoc Networks

2021 ◽  
Vol 9 (VII) ◽  
pp. 3130-3134
Author(s):  
Partha Sarathi Dutta
Keyword(s):  
Outage Probability ◽  
Power Allocation ◽  
Ad Hoc ◽  
Closed Form Solution ◽  
Form Solution ◽  
Cross Layer ◽  
Transmission Power ◽  
Routing Metric ◽  
Multihop Ad Hoc Networks ◽  
End To End

In this study, cross-layer approach for joint routing and power allocation problem is formulated in an optimization framework for end-to-end outage minimization under the constraint of total permissible transmission power. A closed form solution for optimal transmission power is obtained following the extraction of routing metric. The scheme is referred as minimum end-to-end outage probability (MEO) strategy. A distributed implementation of the proposed strategy is also presented. Simulation results prove that our proposed MEO routing and power allocation strategy succeeds in achieving significant improvement of end-to-end outage probability over MEO routing and equal power allocation scheme.

scholarly journals Geometric Nonlinear Analysis of Composite Stiffened Panels Using Variational Asymptotic Method

AIAA Journal ◽  
2020 ◽  
Vol 58 (9) ◽  
pp. 4189-4203
Author(s):  
K. Jagath Narayana ◽  
Ramesh Gupta Burela ◽  
Sathiskumar Anusuya Ponnusami ◽  
Dineshkumar Harursampath
Keyword(s):  
Nonlinear Analysis ◽  
Asymptotic Method ◽  
Stiffened Panels ◽  
Geometric Nonlinear ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Geometric Nonlinear Analysis

Proper Inclusion of Interiorly Applied Loads With Beam Theory

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Jimmy C. Ho ◽  
Wenbin Yu ◽  
Dewey H. Hodges
Keyword(s):  
Asymptotic Method ◽  
Beam Theory ◽  
Elliptic Cylinder ◽  
Conventional Approach ◽  
Body Forces ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Elasticity Solutions ◽  
Precise Distribution

An error is introduced by the conventional approach of applying beam theory in the presence of interiorly applied loads. This error arises from neglecting the influence of the precise distribution of surface tractions and body forces on the warping displacements. This paper intends to show that beam theory is capable of accounting for this influence on warping and accomplishes this by the variational asymptotic method. Correlations between elasticity solutions and beam solutions provide not only validations of beam solutions, but also illustrate the resulting errors from the conventional approach. Correlations are provided here for an isotropic parallelepiped undergoing pure extensional deformations and for an isotropic elliptic cylinder undergoing pure torsional deformations.

Prediction of Mechanical Properties of Microcellular Plastics Using the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH) Method

2013 ◽  
Author(s):  
Emily Yu ◽  
Lih-Sheng Turng
Keyword(s):  
Mechanical Properties ◽  
Asymptotic Method ◽  
Thermoplastic Polyurethane ◽  
Three Dimensional ◽  
Unit Cell ◽  
Element Analysis ◽  
Microcellular Plastics ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Injection Molded

This work presents the application of the micromechanical variational asymptotic method for unit cell homogenization (VAMUCH) with a three-dimensional unit cell (UC) structure and a coupled, macroscale finite element analysis for analyzing and predicting the effective elastic properties of microcellular injection molded plastics. A series of injection molded plastic samples — which included polylactic acid (PLA), polypropylene (PP), polystyrene (PS), and thermoplastic polyurethane (TPU) — with microcellular foamed structures were produced and their mechanical properties were compared with predicted values. The results showed that for most material samples, the numerical prediction was in fairly good agreement with experimental results, which demonstrates the applicability and reliability of VAMUCH in analyzing the mechanical properties of porous materials. The study also found that material characteristics such as brittleness or ductility could influence the predicted results and that the VAMUCH prediction could be improved when the UC structure was more representative of the real composition.

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