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  • Effect of Residual Stresses on Wave Propagation in Adhesively Bonded Multilayered MEMS Structures
  • Abstract The paper investigates propagation of stationary plane longitudinal and transverse waves along the layers in adhesively bonded multilayered structures for MEMS applications in the presence of residual stresses. The multilayered structure is assumed to consist of the infinite amount of the periodically recurring layers made of two different materials possessing significantly dissimilar properties: conductive metal layer and insulating adhesive layer. It is assumed that the mechanical behaviour of both materials is nonlinear elastic and can be described with the help of the elastic Murnaghan potential depending on the three invariants of strain tensor. The problem is formulated in the framework…
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  • An Advanced Implicit Meshless Approach for the Non-linear Anomalous Subdiffusion Equation
  • Abstract Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation(FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions…
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  • Coupled Thermo-Mechanical Analysis of One-Layered and Multilayered Isotropic and Composite Shells
  • Abstract This work considers the fully coupled thermo-mechanical analysis of one-layered and multilayered isotropic and composite shells. The temperature is assumed a primary variable as the displacement; it is therefore directly obtained from the model and this feature permits the temperature field to be evaluated through the thickness direction. Three problems are analyzed: - static analysis of shells with imposed temperature on the external surfaces; - static analysis of shells subjected to a mechanical load, with the possibility of considering the temperature field effects; - a free vibration problem, with the evaluation of the temperature field effects. In the first problem,…
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  • Numerical Prediction of Young's and Shear Moduli of Carbon Nanotube Composites Incorporating Nanoscale and Interfacial Effects
  • Abstract A hybrid finite element formulation, combining nanoscopic and macroscopic considerations is proposed, for the prediction of the elastic mechanical properties of single walled carbon nanotube (SWCNT)-based composites. The nanotubes are modeled according to the molecular mechanics theory via the use of spring elements, while the matrix is modeled as a continuum medium. A new formulation concerning the load transfer between the nanotubes and matrix is proposed. The interactions between the two phases are implemented by utilizing appropriate stiffness variations describing a heterogeneous interfacial region. A periodic distribution and orientation of the SWCNTs is considered. Thereupon, the nanocomposite is modeled using…
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  • Error Analysis of Various Basis Functions Used in BEM Solution of Acoustic Scattering
  • Abstract In this work, various basis functions used in the Method of Moments or Boundary Element (MoM/BEM) solution of acoustic scattering problems are compared with each other for their performance. Single layer formulation of the rigid bodies is considered in comparison of the solutions. Geometry of a scatterer is descritized using triangular patch modeling and basis functions are defined on triangular patches, edges and nodes for three different solutions. Far field scattering cross sections for different frequencies of incident acoustic wave are compared with the closed form solutions. Also, the errors of the solutions using these three types of basis functions…
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  • MLPG Method Based on Rankine Source Solution for Modelling 3D Breaking Waves
  • Abstract In this paper, the Meshless Local Petrov-Galerkin method based on Rankine source solution (MLPG_R) is further developed to model 3D breaking waves. For this purpose, the technique for identifying free surface particles called Mixed Particle Number Density and Auxiliary Function Method (MPAM) and the semi-analytical technique for estimating the domain integrals for 2D cases are extended to 3D cases. In addition, a new semi-analytical technique is developed to deal with the local spherical surface integrals. The numerical results obtained by the newly developed method will be compared with experimental data available in literature and satisfactory agreement will be shown.
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  • Modelling Elasto-Plasticity Using the Hybrid MLPG Method
  • Abstract Meshless methods continue to generate strong interest as alternatives to conventional finite element methods. One major area of application as yet relatively unexplored with meshless methods is elasto-plasticity. In this paper we extend a novel numerical method, based on the Meshless Local Petrov-Galerkin (MLPG) method, to the modelling of elasto-plastic materials. The extended method is particularly suitable for problems in geomechanics, as it permits inclusion of infinite boundaries, and is demonstrated here on footing problems. The current usage of meshless methods for problems involving plasticity is reviewed and guidance is provided in the choice of various modelling parameters.
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  • Fictitious Time Integration Method of Fundamental Solutions with Chebyshev Polynomials for Solving Poisson-type Nonlinear PDEs
  • Abstract The fictitious time integration method (FTIM) previously developed by Liu and Atluri (2008a) is combined with the method of fundamental solutions and the Chebyshev polynomials to solve Poisson-type nonlinear PDEs. The method of fundamental solutions with Chebyshev polynomials (MFS-CP) is an exponentially-convergent meshless numerical method which is able to solving nonhomogeneous partial differential equations if the fundamental solution and the analytical particular solutions of the considered operator are known. In this study, the MFS-CP is extended to solve Poisson-type nonlinear PDEs by using the FTIM. In the solution procedure, the FTIM is introduced to convert a Poisson-type nonlinear PDE into…
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  • Effect of Patch Mechanical Properties on Right Ventricle Function Using MRI-Based Two-Layer AnisotropicModels of Human Right and Left Ventricles
  • Abstract Right and left ventricle (RV/LV) combination models with three different patch materials (Dacron scaffold, treated pericardium, and contracting myocardium), two-layer construction, fiber orientation, and active anisotropic material properties were introduced to evaluate the effects of patch materials on RV function. A material-stiffening approach was used to model active heart contraction. Cardiac magnetic resonance (CMR) imaging was performed to acquire patient-specific ventricular geometries and cardiac motion from a patient with severe RV dilatation due to pulmonary regurgitation needing RV remodeling and pulmonary valve replacement operation. Computational models were constructed and solved to obtain RV stroke volume, ejection fraction, patch area variations,…
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  • The Lie-Group Shooting Method for Computing the Generalized Sturm-Liouville Problems
  • Abstract We propose a novel technique, transforming the generalized SturmLiouville problem: w'' + q(x,λ)w = 0, a1(λ)w(0) + a2(λ)w'(0) = 0, b1(λ)w(1) + b2(λ)w'(1) = 0 into a canonical one: y'' = f, y(0) = y(1) = c(λ). Then we can construct a very effective Lie-group shooting method (LGSM) to compute eigenvalues and eigenfunctions, since both the left-boundary conditions y(0) = c(λ) and y'(0) = A(λ) can be expressed explicitly in terms of the eigen-parameter λ. Hence, the eigenvalues and eigenfunctions can be easily calculated with better accuracy, by a finer adjusting of λ to match the right-boundary condition y(1) =…
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