Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.11, No.1, pp. 15-32, 2009, DOI:10.3970/cmc.2009.011.015

Abstract Motivated by the evolutionary and dissipative properties of parabolic type partial differential equation (PDE), Liu (2008a) has proposed a natural and mathematically equivalent approach by transforming the quasilinear elliptic PDE into a parabolic one. However, the above paper only considered a rectangular domain in the plane, and did not treat the difficulty arisen from the quasilinear PDE defined in an arbitrary plane domain. In this paper we propose a new technique of internal and boundary residuals in a fictitious rectangular domain, which are driving forces for the ordinary differential equations based on the Fictitious Time Integration Method (FTIM). Several numerical… More >

J.H. Tian^1,2, X. Han², S.Y. Long³, G.Q. Xie⁴

CMC-Computers, Materials & Continua, Vol.10, No.3, pp. 229-242, 2009, DOI:10.3970/cmc.2009.010.229

Abstract A heat conduction analysis of the functionally graded material (FGM) plates has been investigated based on the hybrid numerical method (HNM). HNM combines the layer element method with the method of Fourier transforms and proves to be efficient and reliable. The FGM plates are infinite large and the material properties vary continuously through thickness. The heat source continually acted one the FGM plates. The temperature distribution of the FGM plates is obtained in different time and different position. Some useful results for heat conduction problems are shown in figures. This article applies HNM to heat conduction firstly and provides us… More >

Deepak A Apte¹, Ranjan Ganguli^1,2

CMC-Computers, Materials & Continua, Vol.10, No.2, pp. 139-162, 2009, DOI:10.3970/cmc.2009.010.139

Abstract The influence of electric field and temperature on power consumption of piezoelectric actuated integrated structure is studied by using a single degree of freedom mass-spring-damper system model coupled with a piezoactuator. The material lead zirconate titanate, is considered as it is capable of producing relatively high strains (e.g., 3000με). Actuators are often subject to high electric fields to increase the induced strain produced, resulting in field dependant piezoelectric coefficient d₃₁, dielectric coefficient ε₃₃ and dissipation factor δ. Piezostructures are also likely to be used across a wide range of temperatures in aerospace and undersea operations. Again, the piezoelectric properties can… More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.10, No.1, pp. 97-116, 2009, DOI:10.3970/cmc.2009.010.097

Abstract A new numerical method is proposed for solving the delay ordinary differential equations (DODEs) under multiple time-varying delays or state-dependent delays. The finite difference scheme is used to approximate the ODEs, which together with the initial conditions constitute a system of nonlinear algebraic equations (NAEs). Then, a Fictitious Time Integration Method (FTIM) is used to solve these NAEs. Numerical examples confirm that the present approach is highly accurate and efficient with a fast convergence. More >

CMC-Computers, Materials & Continua, Vol.10, No.1, pp. 65-96, 2009, DOI:10.3970/cmc.2009.010.065

Abstract This work proposed an alternative formulation for the prediction of martensite start temperature (Ms) of Fe-Mn-Si shape memory alloys (SMAs) depending on the various compositions and heat treatment techniques by using Neural Network (NN) and genetic programming (GP) soft computing techniques. The training and testing patterns of the proposed NN and GP formulations are based on well established experimental results from the literature. The NN and GP based formulation results are compared with experimental results and found to be quite reliable with a very high correlation (R2=0.955 for GEP and 0.999 for NN). More >

J. Ghanbari¹, R. Naghdabadi^1,2

CMC-Computers, Materials & Continua, Vol.10, No.1, pp. 41-64, 2009, DOI:10.3970/cmc.2009.010.041

Abstract Continuum-based modeling of nanostructures is an efficient and suitable method to study the behavior of these structures when the deformation can be considered homogeneous. This paper is concerned about multiscale nonlinear tensorial constitutive modeling of carbon nanostructures based on the interatomic potentials. The proposed constitutive model is a tensorial equation relating the second Piola-Kirchhoff stress tensor to Green-Lagrange strain tensor. For carbon nanotubes, some modifications are made on the planar representative volume element (RVE) to account for the curved atomic structure resulting a non-planar RVE. Using the proposed constitutive model, the elastic behavior of the graphene sheet and carbon nanotube… More >

T. Nishioka¹, S. Tchouikov¹, T. Fujimoto¹

CMC-Computers, Materials & Continua, Vol.3, No.3, pp. 147-154, 2006, DOI:10.3970/cmc.2006.003.147

Abstract In this study, phenomena of multiple branching of dynamically propagating crack are investigated numerically. The complicated paths of cracks propagating in a material are simulated by moving finite element method based on Delaunay automatic triangulation (MFEM BODAT), which was extended for such problems. For evaluation of fracture parameters for propagating and branching cracks switching method of the path independent dynamic J integral was used. Using these techniques the generation phase simulation of multiple dynamic crack branching was performed. Various dynamic fracture parameters, which are almost impossible to obtain by experimental technique alone, were accurately evaluated. More >

K.Y. Volokh ¹

CMC-Computers, Materials & Continua, Vol.3, No.1, pp. 37-42, 2006, DOI:10.3970/cmc.2007.003.037

Abstract Lagrangian or referential equilibrium equations for materials undergoing large deformations are of interest in the developing fields of mechanics of soft biomaterials and nanomechanics. The main feature of these equations is the necessity to deal with the First Piola-Kirchhoff, or nominal, stress tensor which is a two-point tensor referring simultaneously to the reference and current configurations. This two-point nature of the First Piola-Kirchhoff tensor is not always appreciated by the researchers and the total covariant derivative necessary for the formulation of the equilibrium equations in curvilinear coordinates is sometimes inaccurately confused with the regular covariant derivative. Surprisingly, the traditional continuum… More >

Marcello Lappa ¹

CMC-Computers, Materials & Continua, Vol.2, No.1, pp. 51-64, 2005, DOI:10.3970/cmc.2005.002.051

Abstract A possible approach for the investigation of a number of aspects related to the processing of immiscible alloys, made possible by recent progress in both fields of moving boundary (VOF) methods and speed of computers, is discussed. It can capture in a single numerical treatment and without limiting assumptions both macroscopic information (i.e. the macrophysical problem, heretofore treated in terms of population dynamics) and microscopic details (i.e. the microphysical problem, heretofore treated within the framework of boundary integral methods and/or under the assumption of nondeformable drops). The role played by coalescence in changing the Marangoni migration velocity is discussed together… More >