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Modified SFDI for Fully NonlinearWave Simulation
Get PDFIn the Meshless Local Petrove-Galerkin based on Rankine source solution (MLPG-R), a simplified finite difference interpolation (SFDI) scheme was developed for numerical interpolation and gradient calculation (CMES, Vol. 23(2), pp. 75-89). Numerical tests concluded that the SFDI is generally as accurate as the linear moving least square method (MLS) but requires less CPU time. In this paper, a modified SFDI is proposed for numerically modelling of nonlinear water waves, considering the typical feature of the spatial variation of the wave-related parameters. Systematic numerical investigations are carried out and the results indicate that the modification considerably improves the robustness of the SFDI on gradient estimation. Although the scheme is originally derived for meshless method, its feasibility and accuracy in the mesh-based methods are discussed here through the fully nonlinear wave simulation using the Quasi Arbitrary Lagrangian Eulerian Finite Element Method (QALE-FEM), which is based on fully nonlinear potential theory
An Evaluation of Multigrid Acceleration for the Simulation of an Edge FLame in a Mixing Layer
Get PDFA test problem of a laminar edge flame formed in the mixing layer of two initially separated streams of fuel and oxidant is employed to evaluate the performance of multigrid acceleration of the iterative solution of the central difference finite difference scheme approximating the governing energy and species mass fraction conservation equations. The multigrid method was found to be extremely efficient and significantly improved the iterative convergence relative to that of a single grid method. For low to moderate chemical Damkohler numbers, acceleration factors of up to six (6!) times were recorded in the computational time required to obtain iterative convergence with the multigrid method, over that required with the single-grid method to obtain the same level of convergence. Moreover, monotonic convergence was obtained with the multigrid method in cases where the convergence of the single-grid method stalled. However, for large chemical Damkohler numbers of more than a thousand (i.e. very small characteristic chemical reaction times) and three levels of grid refinement the advantage of application of the multigrid method was seriously degraded due to the necessity to dampen errors stemming from the highly nonlinear chemical source terms on coarse grid levels of the multigrid hierarchy
An Improved Technique to Generate RogueWaves in Random Sea
Get PDFThis paper presents an improved technique to generate rogue (freak) waves embedded in random sea based on the approach proposed by Kribel and Alsina (2000). In this method, a part of the wave energy is focused using the temporal-spatial focusing approach to generate an extreme transient wave and the rest behaves randomly. By introducing a correction term, the improved technique removes the numerical.ly spurious fluctuations of the spectra in the existing approach. Various effects of the correction are investigated numerically by using the second-order wave theory and two existing numerical. methods based on the fully nonlinear potential theory (FNPT), including the improved Spectral Boundary Integral (SBI) method and the Quasi Arbitrary Lagrangian- Eulerian Finite Element Method (QALE-FEM). The discussions are mainly focused on (1) the effectiveness of the correction on retaining the features of the specified wave spectrum; and (2) the effects of the correction on the probability of the maximum wave heights
A Micromechanical Model for Estimating the Effective Stiffness of a Pair of Micro-cracked Interfaces in an Orthotropic Trimaterial under Inplane Deformations
Get PDFA micromechanical model is proposed here for estimating the effective stiffness of a pair of parallel microscopically damaged interfaces in a trimaterial under inplane elastostatic deformations. The trimaterial is made of an orthotropic thin layer sandwiched between two orthotropic half-spaces. The microscopically damaged interfaces are modeled using periodically distributed interfacial micro-cracks. The micromechanical model is formulated and numerically solved in terms of hypersingular boundary integro-differential equations. The effects of the width of the thin layer, the micro-crack densities of the two interfaces and the material constants of the thin layer and the two half-spaces on the effective stiffness coefficients are investigated
Are Higher-Order Theories and Layer-wise Zig-Zag Theories Necessary for N-Layer Composite Laminates?
Get PDFAlthough “higher-order” and layer-wise “higher-order” plate and shell
theories for composite laminates are widely popularized in the current literature,
they involve (1) postulating very complex assumptions of plate/shell kinematics in
the thickness direction, (2) defining generalized variables of displacements, strains,
and stresses, and (3) developing very complex governing equilibrium, compatibility,
and constitutive equations in terms of newly-defined generalized kinemaic and
generalized kinetic variables. Their industrial applications are thus hindered by
their inherent complexity, and the fact that it is difficult for end-users (front-line
structural engineers) to completely understand all the newly-defined FEM DOFs
in higher-order and layer-wise theories. In an entirely different way, the authors
developed very simple lowest-order (8-node hexahedral), and higher-order
(32-node hexahedral) 3-D continuum solid-shell elements, based on the theory of
3D solid mechanics, for static and dynamic analyses of composite laminates. The
shear-locking of the lower-order 8-node hexahedral element is alleviated by independently
assuming locking-free strain fields for each element. Over-integration
is used to evaluate the element stiffness matrices of laminated structures with an
arbitrary number of laminae, while only one element is used in the thickness direction
without increasing the number of degrees of freedom. A stress-recovery
approach is used to compute the distribution of transverse stresses by considering
the equations of 3D elasticity. Comprehensive numerical results are presented for
static, free vibration, and transient analyses of different laminated plates and shells,
which agree well with existing solutions in the published literature, or solutions
of very-expensive 3D models (where 3D elements are used to model each layer)
by using commercial FEM codes. Because the proposed methodology merely involves
simple displacement DOFs at each node, relies only on the simple theory of
solid mechanics, and is capable of accurately and efficiently predicting the static and dynamical behavior of composite laminates in a very simple and cost-effective
manner, it is thus believed by the authors that the development of “higher-order” or
“layer-wise higher-order” theories are not entirely necessary for analyses of laminated
plates and shells
The Influence of Non-Homogeneous Material Properties on ElasticWave Propagation in Fluid-Filled Boreholes
Get PDFThis paper implements a numerical method based on the mutual coupling of the boundary element method (BEM) and the meshless local Petrov-Galerkin (MLPG) method to simulate elastic wave propagation in fluid-filled boreholes. The fluid-solid interaction is solved in the frequency domain assuming longitudinally invariant geometry in the axial direction (2.5D formulation).
This model is used to assess the influence of the non-homogeneous material properties of a borehole wall that can be caused by a damaged zone, construction process or the ageing of material. The BEM is used to model propagation within the unbounded homogeneous domain and the fluid domain inside the borehole and the MLPG method is used to simulate the confined, non-homogeneous, surrounding damaged borehole. The advantages of MLPG in modeling non-homogeneous bounded media and the advantage of BEM in modeling unbounded homogeneous material are thus exploited. The coupling of the two numerical techniques is accomplished directly at the nodal points located at the common interface. Boundary conditions at the interfaces are imposed through the collocation of continuity equations at the interface by means of the moving least-squares (MLS) scheme. At the solid-solid interface, continuity of stresses and displacements is imposed, while continuity of normal stresses and displacements and null shear stress are prescribed at the fluid-solid interface.
The validity of the coupled BEM-MLPG approach is confirmed against the results provided by an analytical solution developed for a circular multi-layered subdomain, in which the central fluid domain is surrounded by a circular non-homogeneous elastic region whose material properties vary radially. Finally, the example of an unbounded medium containing two fluid-filled boreholes excited by a blast load is used to illustrate the applicability of the proposed model
First-principles Calculation of Interfacial Adhesion Strength and Electromigration for the Micro-bump Interconnect of 3D Chip Stacking Packaging
Get PDFThis study aims at exploring the interfacial adhesion strength between solder bump and four typical under bump metallurgies (UBMs), i.e., Cu/Ni, Cu/TiW, Cu/Ni/Cr and /Cu/V/Cr, at atomistic scale. The average bond length and interfacial adhesion stress of the Sn-3.5Ag/Cu/Ni, Sn-3.5Ag/Cu/TiW, Sn-3.5Ag/Cu/Ni/Cr and Sn-3.5Ag/Cu/V/Cr micro-bump interconnects are calculated through the firstprinciples density functional theory (DFT) calculation to estimate the interfacial adhesion strength between the solder bump and UBMs. In addition, by investigating the electric field effect on the average bond length and adhesive stress, the combination of solder bump and UBM with better interfacial adhesion strength and electromigration resistance ability can be determined. The results show that the interfacial adhesion strength between solder bump and wetting layer is much weaker than those of other interfaces, implying that the interfacial failure, induced by the electromigration, is likely to occur at the interface between solder bump and wetting layer. It is also found that the Sn-3.5Ag/Cu/Ni micro-bump interconnect would possess much stronger interfacial adhesion strength at the interface between solder bump and wetting layer than the other micro-bump interconnects. In addition, in comparison with the TiW and V metals, the Ni metal as the diffusion barrier layer can yield much stronger interfacial adhesion strength with wetting layer. Finally, as the adhesion layer is made of Cr metal, the Ni metal, acting as diffusion barrier layer, would hold much stronger interfacial adhesion strength than that of V metal
A Multiscale Method Based on the Fibre Configuration Field, IRBF and DAVSS for the Simulation of Fibre Suspension Flows
Get PDFIn this paper, an Integrated Radial Basis Function (IRBF)-based multiscale method is used to simulate the rheological properties of dilute fibre suspensions. For the approach, a fusion of the IRBF computation scheme, the Discrete Adaptive Viscoelastic Stress Splitting (DAVSS) technique and the Fibre Configuration Field has been developed to investigate the evolution of the flow and the fibre configurations through two separate computational processes. Indeed, the flow conservation equations, which are expressed in vorticity-stream function formulation, are solved using IRBF-based numerical schemes while the evolution of fibre configuration fields governed by the Jeffery’s equation is captured using the principle of Brownian Configuration Fields. The two procedures are coupled together by the Lipscomb expression which is used to determine the fibre stress of dilute fibre suspensions. Owing to advantages of the IRBF scheme and the DAVSS technique, the present method yields a more accurate solution and faster convergence rate. The simulation method is verified and its capability is demonstrated with the fibre suspension flows through two parallel plates, a circular tube and the 4:1 and 4.5:1 axisymmetric contraction geometries which are usually chosen to test a numerical method because of the challenging nature of these problems
MultivariableWavelet Finite Element for Plane Truss Analysis
Get PDFPlane truss is widely used in mechanical engineering, building engineering and the aerospace engineering et al.. The precisely analysis of plane truss is very important for structural design and damage detection. Based on the generalized variational principle and B spline wavelet on the interval (BSWI), the multivariable wavelet finite element for plane truss is constructed. First, the wavelet axial rod element and the multivariable wavelet Euler beam element are constructed. Then the multivariable plane truss element can be obtained by combining these two elements together. Comparing with the traditional method, the generalized displacement and stress are treated as independent variables in multivariable method, so differentiation and integration are avoided in calculation, the efficiency and precision can be improved. Furthermore, compared with commonly used Daubechies wavelet, BSWI has explicit expression and excellent approximation property, which further guarantees satisfactory results. The efficiency of the constructed multivariable wavelet elements is validated through several numerical examples in the end
On the Use of a Lattice Model for Analyzing of In-Plane Vibration of Thin Plates
No full textIn this paper, a novel approach for simulating in-plane vibration of thin plates is proposed. It is based on the spectral element method (SEM) used within a lattice modeling framework. First, derivation of a frequency dependent dynamic stiffness matrix for a spectral beam element is presented. Then, the lattice modeling concept is introduced. In the model, the two-dimensional plate is discretized as a set of (one dimensional) spectral beam elements connected at the ends. The proposed approach is then used for modal analysis of rectangular plates of different aspect ratios (1 and 2) and boundary conditions (completely free and clamped). Simulated natural frequencies and modal shapes are compared to results available in the literature. It was found that the proposed model can reasonably reproduce low natural frequencies (in most cases within 10%) and modal shapes. Future work will focus on the use of the model as an aid in non-destructive testing of structures