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  • On the Energy Release Rate at the Crack Tips in a Finite Pre-Strained Strip
  • Abstract The influence of the initial finite stretching or compressing of the strip containing a single crack on the Energy Release Rate (ERR) and on the SIF of mode I at the crack tips is studied by the use of the Three-Dimensional Linearized Theory of Elasticity. It is assumed that the edges of the crack are parallel to the face planes of the strip and the ends of the strip are simply supported. The initial finite strain state arises by the uniformly distributed normal forces acting at the ends of the strip. The additional normal forces act on the edges of…
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  • A Three-dimensional Adaptive Strategy with Uniform Background Grid in Element-free Galerkin Method for Extremely Large Deformation Problems
  • Abstract A novel three-dimensional adaptive element-free Galerkin method (EFGM) based on a uniform background grid is proposed to cope with the problems with extremely large deformation. On the basis of this uniform background grid, an interior adaptive strategy through an error estimation within the analysis domain is developed. By this interior adaptive scheme, additional adaptive nodes are inserted in those regions where the solution accuracy needs to be improved. As opposed to the fixed uniform background grid, these inserted nodes can move along with deformation to describe the particular local deformation of the structure. In addition, a triangular surface technique is…
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  • A New Quasi-Boundary Scheme for Three-Dimensional Backward Heat Conduction Problems
  • Abstract In this study, we employ a semi-analytical scheme to resolve the three-dimensional backward heat conduction problem (BHCP) by utilizing a quasi-bound -ary concept. First, the Fourier series expansion method is used to estimate the temperature field u(x, y, z, t) at any time t < T. Second, we ponder a direct regularization by adding an extra term a(x, y, z, 0) to transform a second-kind Fredholm integral equation for u(x, y, z, 0). The termwise separable property of the kernel function allows us to acquire a closed-form regularized solution. In addition, a tactic to determine the regularization parameter is recommended.…
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  • Nearest Particle Distance and the Statistical Distribution of Agglomerates from a Model of a Finite Set of Particles
  • Abstract The structural analysis of a particulate composite with randomly distributed hard spheres is presented based on a model proposed earlier. The structural factors considered include the distribution of interparticle distances and the conditions for particle agglomeration. The interparticle distance was characterized by the nearest particle distance (NPD) and the distance derived from Delaunay triangulation (DT). The distances were calculated for every particle in the particle set and analyzed in the form of a cumulative distribution function (CDF). The CDF provides two parameters: the representation of particles which are in very close proximity to their neighbors and the most frequent distance…
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  • Vibration and Buckling of Truss Core Sandwich Plates on An Elastic Foundation Subjected to Biaxial In-plane Loads
  • Abstract Truss-core sandwich plates are thin-walled structures comprising a truss core and two thin flat sheets. Since no direct analytical solution for the dynamic response of such structures exists, the complex three dimensional (3D) systems are idealized as equivalent 2D homogeneous continuous plates. The macroscopic effective bending and transverse shear stiffness are derived. Two representative core topologies are considered: pyramidal truss core and tetrahedral truss core. The first order shear deformation theory is used to study the flexural vibration of a simply supported sandwich plate. The buckling of the truss core plate on an elastic foundation subjected to biaxial in-plane compressive…
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  • A 3D Constitutive Model for Magnetostrictive Materials
  • Abstract This paper is concerned with a 3-D general constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive materials. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A set of closed and analytical expressions of the constitutive relationships for the magnetostrictive materials are obtained, in which all parameters can be determined by those measurable experiments in mechanics and physics. Then the model can be simplified to two cases, i.e. magnetostrictive rods and films. It is found that the predictions from this model are in good accordance with the experimental data including both rods and films.…
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  • Solution of Inverse Boundary Optimization Problem by Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm
  • Abstract The inverse boundary optimization problem, governed by the Helmholtz equation, is analyzed by the Trefftz method (TM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the inverse boundary optimization problem, the position for part of boundary with given boundary condition is unknown, and the position for the rest of boundary with additionally specified boundary conditions is given. Therefore, it is very difficult to handle the boundary optimization problem by any numerical scheme. In order to stably solve the boundary optimization problem, the TM, one kind of boundary-type meshless methods, is adopted in this study, since it can avoid the…
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  • The Spring-Damping Regularization Method and the Lie-Group Shooting Method for Inverse Cauchy Problems
  • Abstract The inverse Cauchy problems for elliptic equations, such as the Laplace equation, the Poisson equation, the Helmholtz equation and the modified Helmholtz equation, defined in annular domains are investigated. The outer boundary of the annulus is imposed by overspecified boundary data, and we seek unknown data on the inner boundary through the numerical solution by a spring-damping regularization method and its Lie-group shooting method (LGSM). Several numerical examples are examined to show that the LGSM can overcome the ill-posed behavior of inverse Cauchy problem against the disturbance from random noise, and the computational cost is very cheap.
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  • A Simple Procedure to Develop Efficient & Stable Hybrid/Mixed Elements, and Voronoi Cell Finite Elements for Macro- & Micromechanics
  • Abstract A simple procedure to formulate efficient and stable hybrid/mixed finite elements is developed, for applications in macro- as well as micromechanics. In this method, the strain and displacement field are independently assumed. Instead of using two-field variational principles to enforce both equilibrium and compatibility conditions in a variational sense, the independently assumed element strains are related to the strains derived from the independently assumed element displacements, at a finite number of collocation points within the element. The element stiffness matrix is therefore derived, by simply using the principle of minimum potential energy. Taking the four-node plane isoparametric element as an…
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  • Dynamic Failure Behavior of Nanocrystalline Cu at Atomic Scales
  • Abstract Large-scale molecular dynamics (MD) simulations are used to investigate the effects of microstructure and loading conditions on the dynamic failure behavior of nanocrystalline Cu. The nucleation, growth, and coalescence of voids is investigated for the nanocrystalline metal with average grain sizes ranging from 6 nm to 12 nm (inverse Hall-Petch regime) for conditions of uniaxial expansion at constant strain rates ranging from 4x107 s - 1 to 1010 s - 1. MD simulations suggest that the evolution of voids can be described in two stages: The first stage corresponds to the nucleation of voids and the fast linear initial growth…
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