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Solutions of a Crack Interacting with Tri-Material Composite in Plane Elasticity
No full textIn this paper a crack interacting with tri-material composite under a remote uniform tensile load is solved in plane elasticity. An edge dislocation distribution along the prospective site of the crack together with the principle of superposition is used to model a crack. The resulting singular integral equation with logarithmic singular kernels for a line crack is then established. The singular integral equation is solved numerically by modeling a crack in place of several segments. Linear interpolation formulae with undetermined coefficients are applied to approximate the dislocation distribution along the elements, except at vicinity of crack tip where the dislocation distribution preserves a square-root singularity. Once the undetermined dislocation coefficients are solved, the mode-I and mode-II stress intensity factors can be obtained. Some numerical results are performed to show the effects of material property combinations and geometric parameters on the normalized mode-I and mode-II stress intensity factors
FEM/Wideband FMBEM Coupling for Fluid-Structure Interaction Problem and 2D Acoustic Design Sensitivity Analysis
Get PDFA coupling algorithm based on the finite element method and the wideband fast multipole boundary element method (FEM/wideband FMBEM) is proposed for the simulation of fluid-structure interaction and structural-acoustic sensitivity analysis using the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. The FEM/Wideband FMBEM algorithm makes it possible to predict the effects of arbitrarily shaped vibrating structures on the sound field numerically. Numerical examples are presented to demonstrate the validity and efficiency of the proposed algorithm
Universal Reliability Method for Structural Models with Both Random and Fuzzy Variables
Get PDFThe conventional probabilistic reliability model for structures is based on the “probability assumption” and “binary-state assumption”. These assumptions are often offset the reality of practical engineering and lead to a wrong conclusion. In fact, besides randomness, fuzziness which is different from randomness in nature is also a prevalent uncertainty factor and plays an important role in structural reliability assessment. In this paper, a novel structural reliability model with random variables and fuzzy variables is established by using the fuzzy set theory, possibility theory and probability measure for fuzzy events, based on the “mixed probability and possibility assumption” and “fuzzy state assumption”. The presented universal structural reliability model can be regarded as the unification of probability reliability theory and possibility reliability theory. The universal reliability model can degenerate into probabilistic reliability model or possibility reliability model spontaneously for pure random basic variables or fuzzy basic variables. The Monte-Carlo simulation combing with optimization method is applied to calculate the failure probability of the structures. Numerical examples revealed the feasibility of the proposed reliability model for structures
Numerical Evalution of Eshelby’s Tensor of Anisotropic Ferromagnetic Shape Memory Alloy and Its Influence on Magnetic Field-induced Strain
Get PDFSingle crystal ferromagnetic shape memory alloy is a kind of new intelligent materials, it shows obvious anisotropy. Micromechanics theory has been used to analyze the whole mechanical behaviors of this material. However, Eshelby’s tensor of this material which plays an important role has still not solved efficiently. Based on the existing micromechanics constitutive model, this paper analyzes the numerical calculation formula of Eshelby’s tensor of anisotropic ferromagnetic shape memory alloy. Adopting the way of Gauss integral, the optimal Gaussian integral points for different inclusion shapes and the corresponding numerical solution of Eshelby’s tensor are obtained.Furthermore, the influence of inclusion shapes on interaction energy and magnetic field-induced strains of Ni2MnGa single crystal is analyzed.It shows that the interaction energy of penny inclusion of ferromagnetic shape memory alloy is the maximum. The magnetic field-induced strain of spherical inclusion is the most close to experimental data. The above results can provide theoretical guidance for design and use of ferromagnetic shape memory alloy
Interactions of Three Parallel Square-Hole Cracks in an Infinite Plate Subjected to Internal Pressure
Get PDFBy using a hybrid displacement discontinuity method, the interactions of three parallel square-hole cracks in an infinite plate subjected to internal pressure are investigated in this paper. Numerical examples are included to illustrate that the numerical approach is very simple and effective for calculating the stress intensity factors (SIFs) of complex plane crack problems. Many numerical results of the SIFs are given and discussed. It is found that a square hole has a shielding effect on crack(s) emanating from the hole. The finding perhaps has an important meaning in engineering
Numerical Solutions for Free Vibration Analysis of Thick Square Plates by the BEM
Get PDFIn this work, the BEM is applied to obtain the numerical solutions for free vibration analysis of thick square plates with two edges simply supported or clamped, and the other two edges free. A formulation based on Reissner’s theory is used here, which includes the contribution of the additional translational inertia terms to the integral equation of displacements and internal forces. The boundary element method is used to discretize the space, where it is employed the static fundamental solution. In literature, the responses for the kind of problem addressed here are very important in the hydroelastic analysis of very large floating structures (VLFS) which are commonly modeled as plates with free edges. To verify the accuracy this formulation some analyses are presented at the end of the paper
Numerical Study of Polymer Composites in Contact
Get PDFA boundary element based formulation is applied to study numerically the tribological behavior of fiber-reinforced plastics (FRP) under different frictional contact conditions, taking into account the micromechanics of FRP. Micromechanical models presented consider continuous and short fiber reinforced plastics configurations. The Boundary Element Method (BEM) with an explicit approach for fundamental solutions evaluation is considered for computing the elastic influence coefficients. Signorini’s contact conditions and an orthotropic law of friction on the potential contact zone are enforced by contact operators over the augmented Lagrangian. The proposed methodology is applied to study carbon FRP under frictional contact. The obtained numerical results illustrate how the fiber orientation, fiber volume fraction, fiber length and sliding orientation affect the normal and tangential contact compliance, as well as the contact traction distribution
SPH and ALE Formulations for Fluid Structure Coupling
Get PDFSimulation of Fluid Structure Interaction FSI, problems becomes more and more the focus of computational engineering, where FEM (Finite element Methods) for structural mechanics and Finite Volume for CFD are dominant. New formulations have been developed for FSI applications using mesh free methods as SPH method, (Smooth Particle Hydrodynamic). Up to these days very little has been done to compare different methods and assess which one would be more suitable. For small deformation, FEM Lagrangian formulation can solve structure interface and material boundary accurately; the main limitation of the formulation is high mesh distortion for large deformation and moving structure. One of the commonly used approach to solve these problems is the ALE formulation which has been used with success in the simulation of fluid structure interaction with large structure motion such as sloshing fuel tank in automotive industry and bird impact in aeronautic industry. For some applications, including bird impact and high velocity impact problems, engineers have switched from ALE to SPH method to reduce CPU time and save memory allocation.
In this paper the mathematical and numerical implementation of the ALE and SPH formulations are described. From different simulation, it has been observed that for the SPH method to provide similar results as ALE or Lagrangian formulations, the SPH meshing, or SPH spacing particles needs to be finer than the ALE mesh. To validate the statement, we perform a simulation of a shock wave propagation generated by explosive detonation. For this simple problem, the particle spacing of SPH method needs to be at least two times finer than ALE mesh. A contact algorithm is performed at the fluid structure interface for both SPH and ALE formulations
Numerical Modeling of Skin Tissue Heating Using the Interval Finite Difference Method
Get PDFNumerical analysis of heat transfer processes proceeding in a nonhomogeneous biological tissue domain is presented. In particular, the skin tissue domain subjected to an external heat source is considered. The problem is treated as an axially-symmetrical one (it results from the mathematical form of the function describing the external heat source). Thermophysical parameters of sub-domains (volumetric specific heat, thermal conductivity, perfusion coefficient etc.) are given as interval numbers. The problem discussed is solved using the interval finite difference method basing on the rules of directed interval arithmetic, this means that at the stage of FDM algorithm construction the mathematical manipulations are realized using the interval numbers. In the final part of the paper the results of numerical computations are shown, in particular the problem of admissible thermal dose is analyzed
Differential Orientation of 10T1/2 Mesenchymal Cells on Non-Uniform Stretch Environments
Get PDFNon-uniform stress and strain fields are prevalent in many tissues in vivo, and often exacerbated by disease or injury. These mechanical gradients potentially play a role in contributing to pathological conditions, presenting a need for experimental tools to allow investigation of cell behavior within non-uniformly stimulated environments. Herein, we employ two in vitro cell-stretching devices (one previously published; one newly presented) capable of subjecting cells to cyclic, non-uniform stretches upon the surface of either a circular elastomeric membrane or a cylindrical PDMS tube. After 24 hours of cyclic stretch, 10T1/2 cells on both devices showed marked changes in long-axis orientation, with tendencies to align parallel to the direction of minimal deformation. The degree of this response varied depending on location within the stretch gradients. These results demonstrated the feasibility of conducting cell mechanobiology investigations with the two novel devices, while also highlighting the experimental capabilities of non-uniform mechanical environments for these types of studies. Such capabilities include robust data collection for developing mechanobiological dose-response curves, signal threshold identification, and potential spatial targeting for drug delivery