Showing papers in "Cmc-computers Materials & Continua in 2007"
TL;DR: In this article, the authors describe the foundation and properties of the so-called dynamic boundary particles (DBPs), which share the same equations of continuity and state as the moving particles placed inside the domain, although their positions and velocities remain unaltered in time.
Abstract: Smoothed Particle Hydrodynamics is a purely Lagrangian method that can be applied to a wide variety of fields. The foundation and properties of the so called dynamic boundary particles (DBPs) are described in this paper. These boundary particles share the same equations of continuity and state as the moving particles placed inside the domain, although their positions and velocities remain unaltered in time or are externally prescribed. Theoretical and numerical calculations were carried out to study the collision between a moving particle and a boundary particle. The boundaries were observed to behave in an elastic manner in absence of viscosity. They allow the fluid particles to approach till a critical distance depending on the energy of the incident particle. In addition, a dam break confined in a box was used to check the validity of the approach. The good agreement between experiments and numerical results shows the reliability of DBPs. Keyword: Meshfree methods, SPH, smoothed particle hydrodynamics, boundary conditions
351 citations
39 citations
34 citations
TL;DR: In this paper, a meshless method based on radial-basis function networks (RBFNs) was proposed for the static analysis of moderately-thick laminated composite plates using the first-order shear deformation theory.
Abstract: This paper reports a meshless method, which is based on radial-basis-function networks (RBFNs), for the static analysis of moderately-thick laminated composite plates using the first-order shear deformation theory. Integrated RBFNs are employed to represent the field variables, and the governing equations are discretized by means of point collocation. The use of integration rather than conventional differentiation to construct the RBF approximations significantly stabilizes the solution and enhances the quality of approximation. The proposed method is verified through the solution of rectangular and non-rectangular composite plates. Numerical results obtained show that the method achieves a very high degree of accuracy and a fast convergence rate.
30 citations
TL;DR: By using a meshless regularized in-tegral equation method (MRIEM), the solution of elastic torsion problem of a uniform bar with ar- bitrary cross-section is presented by the first kind Fredholm integral equation on an artificial circle, which just encloses the bar's cross-sectional as mentioned in this paper.
Abstract: By using a meshless regularized in- tegral equation method (MRIEM), the solution of elastic torsion problem of a uniform bar with ar- bitrary cross-section is presented by the first kind Fredholm integral equation on an artificial circle, which just encloses the bar's cross-section. The termwiseseparableproperty ofkernel functional- lows us to obtain the semi-analytical solutions of conjugate warping function and shear stresses. A criterion is used to select the regularized parame- ter accordingtotheminimum principleof Laplace equation. Numerical examples show the effec- tiveness of the new method in providing very ac- curate numerical solutions as compared with the exact ones. Keyword: Laplace equation, Elastic torsion, Fredholm integral equation, Lavrentiev regular- ization, Fourier series, Artificial circle
28 citations
TL;DR: In this article, a simple but efficient and accurate four-node quadrilateral element for models of laminated, anisotropic plate behavior within the framework of the first-order shear deformation theory is presented.
Abstract: This paper reports the development of a simple but efficient and accurate four-node quadrilateral element for models of laminated, anisotropic plate behaviour within the framework of the first-order shear deformation theory. The approach incorporates the strain smoothing method for mesh-free conforming nodal integration into the conventional finite element techniques. The membrane-bending part of the element stiffness matrix is calculated by the line integral on the boundaries of the smoothing elements while the shear part is performed using an independent interpolation field in the natural co-ordinate system. Numerical results show that the element offered here is locking-free for extremely thin laminates, reliable and accurate, and easy to implement. Its convergence properties are insensitive to mesh distortion, thickness-span ratios, lay-up sequence and degree of anisotropy.
16 citations
TL;DR: In this article, the authors investigated the effect of damage on beams with fixed boundary conditions using Fourier analysis of the mode shapes in spatial domain and found that the Fourier coefficients, especially the higher harmonics, are sensitive to both damage size and location and amplify the changes in the mode shape due to the damage.
Abstract: This paper investigates the effect of damage on beams with fixed boundary conditions using Fourier analysis of the mode shapes in spatial domain. A finite element model is used to obtain the mode shapes of a damaged fixed-fixed beam. Then the damaged beams are studied using a spatial Fourier analysis. This approach contrasts with the typical time domain application of Fourier analysis for vibration problems. It is found that damage causes considerable change in the Fourier coefficients of the mode shapes. The Fourier coefficients, especially the higher harmonics, are found to be sensitive to both damage size and location and amplify the changes in the mode shape due to the damage. Therefore, we formulate a damage index in the form of a vector of Fourier coefficients which is robust and unique for a given damage size and damage location. The effect of noise in the mode shape data is considered and it is found that Fourier coefficients provide a useful indication of damage even in the presence of noise. Various damage levels are considered and it is found that higher modes are needed to detect small amount of damage.
16 citations
TL;DR: In this article, a numerical simulation of the formation and evolution of strain localization in elasto-thermo-viscoplastic materials (adiabatic shear band) by the indirect/integral radial basis function network (IRBFN) method is presented.
Abstract: This paper presents a numerical simulation of the formation and evolution of strain localization in elasto-thermo-viscoplastic materials (adiabatic shear band) by the indirect/integral radial basis function network (IRBFN) method. The effects of strain and strain rate hardening, plastic heating, and thermal softening are considered. The IRBFN method is enhanced by a new coordinate mapping which helps capture the stiff spatial structure of the resultant band. The discrete IRBFN system is integrated in time by the implicit fifth-order Runge-Kutta method. The obtained results are compared with those of the Modified Smooth Particle Hydrodynamics (MSPH) method and Chebychev
Pseudo-spectral (CPS) method.
15 citations
TL;DR: In this article, a multi-walled carbon nanotube is modeled as a multiple-elastic cylindrical structure, and the numerical analytical method is adopted to analyze the characteristics of harmonic waves propagating along an anisotropic carbon Nanotube.
Abstract: A multi-walled carbon nanotube is modeled as a multiple-elastic cylindrical structure. The numerical-analytical method is adopted to analyze the characteristics of harmonic waves propagating along an anisotropic carbon nanotube. Each wall of the carbon nanotube is divided into three-nodal-line layer elements. The deflections of two adjacent tubes are coupled through the van der Waals. The governing equation of element is obtained from Hamilton’s principle. A set of system equation of dynamics equilibrium for the entire structure is obtained by the assembling of all the elements. From solution of the eigenvalue equations, the dispersive characteristics, group velocities of multi-walled carbon nanotubes are achieved, and these properties of the six characteristic wave surfaces are also obtained. Keyword: Multi-walled carbon nanotube; elastic wave; group velocity; dispersion; characteristic surfaces
13 citations
TL;DR: In this article, an integral equation technique is developed for the solution of the (i) flexural-torsional buckling and (ii) flexibleural-Torsional vibration problem of Euler-Bernoulli composite beams of constant arbitrarily shaped cross section.
Abstract: In the design of engineering structures, we often come across the analysis of beams subjected to compressive or vibratory loading. This analysis becomes much more complicated in the case the cross section’s centroid does not coincide with its shear center (asymmetric beams), leading to the formulation of the (i) flexural-torsional buckling and (ii) flexural-torsional vibration problems. Also, composite structural elements consisting of a relatively weak matrix material reinforced by stronger inclusions or of materials in contact are of increasing technological importance. Steel beams or columns totally encased in concrete, fiber-reinforced materials or concrete plates stiffened by steel beams are most common examples. The use of the aforementioned structural elements necessitates a rigorous analysis. Although there is an extensive research on the analysis of thin-walled composite beams based on the assumptions of the thin tube theory, to the authors’ knowledge, publications on the solution to the problem of composite beams of constant arbitrarily shaped cross section do not exist. In this investigation an integral equation technique is developed for the solution of the (i) flexural-torsional buckling and (ii) flexural-torsional vibration problem of Euler-Bernoulli composite beams of constant arbitrarily shaped cross section.
13 citations
TL;DR: In this paper, a new, free of MLS-derivatives and non-singular LBIE, method for solving elastic problems is demon-strated, which is accomplished by treating dis- placements and stresses as independent variables through the corresponding local integral equa- tions and considering nodal points located only internally and externally and not on the global boundary of the analyzed elastic structure.
Abstract: Very recently, Vavourakis, Selloun- tos and Polyzos (2006) (CMES: Computer Mod- eling in Engineering & Sciences, vol. 13, pp. 171-184) presented a comparison study on the accuracy provided by five different elastostatic Meshless Local Petrov-Galerkin (MLPG) type formulations, which are based on Local Bound- ary Integral Equation (LBIE) considerations. One of the main conclusions addressed in this pa- per is that the use of derivatives of the Moving Least Squares (MLS) shape functions decreases the solution accuracy of any MLPG(LBIE) for- mulation. In the present work a new, free of MLS-derivatives and non-singular MLPG(LBIE) method for solving elastic problems is demon- strated. This is accomplished by treating dis- placements and stresses as independent variables through the corresponding local integral equa- tions and considering nodal points located only internally and externally and not on the global boundary of the analyzed elastic structure. The MLS approximation scheme for the interpolation of both displacements and stresses is exploited. The essential displacement and traction bound- ary conditions are easily satisfied via the corre- sponding displacement and stress local integral equations. Representative numerical examples that demonstrate the achieved accuracy of the pro- posed MLPG(LBIE) method are provided. Keyword: MLPG4, LBIE, MLS, hypersingu- lar, elastostatics
TL;DR: Zhou et al. as mentioned in this paper presented some simulation results of nonlinear dynamic responses for a laminated composite beam embedded by actuators of the Terfenol-D subjected to external magnetic fields, where the giant magnetostrictive materials utilizing the realignment of magnetic moments in response to applied magnetic fields generate nonlinear strains and forces significantly larger than those generated by other smart materials.
Abstract: This paper presents some simulation results of nonlinear dynamic responses for a laminated composite beam embedded by actuators of the giant magnetostrictive material (Terfenol-D) subjected to external magnetic fields, where the giant magnetostrictive materials utilizing the realignment of magnetic moments in response to applied magnetic fields generate nonlinear strains and forces significantly larger than those generated by other smart materials. To utilize the full potential application of the materials in the function and safety designs, e.g., active control of vibrations, the analysis of dynamic responses is requested in the designs as accurately as possible on the basis of those inherent nonlineary constitutive relations among stain, force and applied magnetic field existed in the materials. Here, a numerical code for the nonlinear vibration of laminated beams is proposed on the basis of a nonlinearly coupling constitutive model which fully behaves for the characteristics what are measured in experiments. It is found from this code that the natural frequency of the laminated beams changes with both the bias magnetic field and the pre-stresses, and the dynamic responses excited by an alternating magnetic field of simple harmonic form display strong nonlinear characteristics, for example, the frequency multiplication and the ultraharmonic resonance phenomena. Keyword: Laminated beams, actuator layers of giant magnetostrictive material, analytical model of nonlinear constitutive model, nonlinear code of 1 Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, P. R. China. 2 College of Information Engineering, China Jiliang University, Hangzhou, 310018, P. R. China. 3 Corresponding author. Tel: 086-0931-8910340; Fax: 0860931-8625576; Email: zhouyh@lzu.edu.cn. vibration analysis, frequency multiplication phenomenon, ultraharmonic resonance phenomenon
TL;DR: In this article, the Lagrangian equilibrium equations in cylindrical and spherical coordinates are derived from the First Piola-Kirchhoff tensor, which is a two-point tensor referring simultaneously to the reference and current configurations.
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 PiolaKirchhoff, 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 mechanics literature does not discuss this issue properly, except for some brief notions on the two-point nature of the Piola-Kirchhoff tensor. We aim at partially filling this gap by giving a full yet simple derivation of the Lagrangian equilibrium equations in cylindrical and spherical coordinates.
TL;DR: In this paper, a damage approach based on a material model with microstructural evolution is presented, where a geometrical modification of the microstructure is allowed to minimize the total energy.
Abstract: A damage approach based on a material model with microstructural evolution is presented. In contrast to phenomenological constitutive laws, the material response is given by mechanisms at the microscale. At first, a micromechanical substructure is chosen, which represents the overall material behaviour. Then the system is described using a micromechanical model. A geometrical modification of the microstructure is allowed to minimize the total energy. Consequently, the global stiffness is reduced. In this context, thermodynamical considerations are based on configurational forces. With the help of the discussed approach, void growth phenomena of materials, which lead to softening behaviour, can be taken into account numerically. In this article, the influence of the microstructure in hyperelastic materials is investigated. Hereby, we discuss evolution methods for small and finite strain problems. Finally, the implementation of this damage approach in an explicit finite element solver is described in detail. Keyword: Configurational Forces, Micromechanics, Damage, Finite Strains, Hyperelasticity.
TL;DR: A multi-resolution adaptive algorithm for solving problems described by partial differential equations based on the collocation method using Fup basis functions, which belong to a class of Rvachev's infinitely differentiable finite functions.
Abstract: In this paper, we present a multi-resolution adaptive algorithm for solving problems described by partial differential equations The technique is based on the collocation method using Fup basis functions, which belong to a class of Rvachev's infinitely differentiable finite functions As it is possible to calculate derivation values of Fup basis functions of high degree in a precise yet simple way, so it is possible to efficiently apply strong formulation procedures The mesh free method developed in this work is named Adaptive Fup Collocation Method (AFCM) The distribution of collocation points within the observed area is changed adaptively, depending on the character of the solution function and the accuracy criteria The numerical procedure is designed through a method of lines (MOL) The basic characteristic of the method is an adaptive multi-resolution approach in solving problems with different spatial and temporal scales and with a desired level of accuracy using the entire family of Fup basis functions Good performance of the proposed method is shown through the numerical examples by using a few general advection dominated problems The results demonstrate that the method is very convenient for solving engineering problems which require extensive computational resources, especially in describing sharp fronts or high gradients and changes of narrow transition zones in space and time
TL;DR: In this article, the authors address the problem of impact on layered fiber composites using ABAQUS and simulate the kinematics of the impact using transient dynamic analysis, employing user defined multi point constraints.
Abstract: The paper addresses the problem of impact on layered fibre composites. The behaviour of composite laminates under impact loading is dependent not only on the velocity but also on the mass and geometry of the impactor. Using micromechanical Mori-Tanaka approach, mechanical properties of the laminate have been calculated utilizing the material constants of the fibre and matrix. General purpose FEM software ABAQUS has been modified by means of user written subroutines for modelling of composite laminate and rigid impactor. The kinematics of the impact has been simulated using transient dynamic analysis. Employing user defined multi point constraints, delamination zones have been modeled and visualised
TL;DR: In this article, a beam element formulation based on higher order shear deformation theory with lateral contraction for axial-flexural-shear coupled deformation in asymmetrically stacked laminated composite beams is presented.
Abstract: A refined $2$-node, $7$ DOF/node beam element formulation is presented in this paper. This formulation is based on higher order shear deformation theory with lateral contraction for axial-flexural-shear coupled deformation in asymmetrically stacked laminated composite beams. In addition to axial, transverse and rotational degrees of freedom, the formulation also incorporates the lateral contraction and its higher order counterparts as degrees of freedom. The element shape functions are derived by solving the static part of the governing equations. The element considers general ply stacking and the numerical results shows that the element exhibits super convergent property. The efficiency of the element in capturing both the static and dynamic inter-laminar stresses is demonstrated. The accuracy of the element to capture free vibration and wave propogation responses with small problem sizes is also demonstrated.
TL;DR: In this paper, a general numerical approach is developed to model the elastic behaviours and failure processes of heterogeneous materials, where the heterogeneous material body is assumed composed of a large number of convex polygon lattices with different phases.
Abstract: A general numerical approach is developed to model the elastic behaviours and failure processes of heterogeneous materials. The heterogeneous material body is assumed composed of a large number of convex polygon lattices with different phases. These phases are locally isotropic and elastic-brittle with the different lattices displaying variable material parameters and a Weibull-type statistical distribution. When the effective strain exceeds a local fracture criterion, the full lattice exhibits failure uniformly, and this is modelled by assuming a very small Young modulus value. An auto-select loading method is employed to model the failure process. The proposed hybrid approach is applied to plane stress problems with fracture patterns and effective loaddisplacement curves presented to illustrate the full failure process. keyword: Heterogeneous materials; Weibull distribution; Elastic-brittle model; Failure process; Finite element method.
TL;DR: In this article, a boundary interpolatable (BI) weight was proposed to fulfill Kronecker delta condition in moving least squares (MLS) approximation along the essential boundary, where the original MLS weight was modified to boundary interpolating weight based on the observation that the support of weight function is exactly the same as the support function of MLS nodal shape function.
Abstract: A novel way is proposed to fulfill Kronecker delta condition in moving least squares (MLS) approximation along the essential boundary. In the proposed scheme, the original MLS weight is modified to boundary interpolatable (BI) weight based on the observation that the support of weight function is exactly the same as the support of MLS nodal shape function. The BI weight is zero along the boundary edges except the edges containing the nodal point associated with the concerned weight. In order to construct the BI weight from the original weight, concept of edge distance function is introduced, and the BI weight construction procedure is presented in detail. Furthermore, it is explained theoretically why the MLS nodal shape functions obtained by BI weights satisfy Kronecker delta condition along the boundary edges. To identify the validity and usefulness of the proposed BI MLS approximation scheme through numerical tests, the scheme is applied to the model problems with rectangular domain and complex shaped domain. Through the tests, theoretical prediction is identified numerically, and it is confirmed that one can handle the essential and natural boundary conditions through the proposed BI MLS scheme in exactly the same manner used in traditional finite element methods. Keyword: BI (Boundary Interpolatable) Weight, Edge Distance Function, Essential Boundary Condition, Kronecker Delta Condition, Moving Least Squares Approximation. 1 Associate Professor, Department of Aerospace Engineering, INHA University, 253 Yonghyun-Dong, Nam-Gu, Incheon, 402-751, Korea. E-mail: cjy@inha.ac.kr
TL;DR: In this paper, a commercially available Finite Element software is used for elasto-plastic analysis of flanging process and the springback is studied varying geometrical, material and friction parameters.
Abstract: One of the important features of flanging process is elastic recovery during unloading leading to springback. The elastic recovery is associated with various tool and material parameters. It is difficult to analytically predict the elastic recovery accurately owing to the complex material deformation behavior. In this investigation, a commercially available Finite Element software is used for elasto-plastic analysis of flanging process. The springback is studied varying geometrical, material and friction parameters. The results of the simulation are validated with a few published experimental results.
TL;DR: In this article, the conjugate gradient method (CGM) is applied in an inverse fin design problem in estimating the optimum shapes for the non-Fourier spine and longitudinal fins based on the desired fin efficiency and fin volume at the specified time.
Abstract: Summary The conjugategradient method (CGM) is applied in an inverse fin design problem in estimating the optimum shapes for the non-Fourier spine and longitudinal fins based on the desired fin efficiency and fin volume at the specified time. One of the advantages in using CGM in the inverse design problem lies in that it can handle problems having a huge number of design parameters easily and converges very fast. The validity of using CGM in solving the present inverse design problem is justified by performing the numerical experiments. Several test cases involving different design fin efficiency, design fin volume, specified time and relaxationtime are considered and examined. Results show that CGM can be utilized successfully in determining the optimum shape of the non-Fourier spine and longitudinalfins.
TL;DR: In this paper, the authors modified the Landau-Lifshitz model into a new one by including a reversible part and an irreversible part accompanying with the switching criteria between these two states.
Abstract: An accurate magnetization requires that both the reversible and irreversible components be modeled. The classical Landau-Lifshitz model deals with only the irreversible component of magnetization. We first subject the LandauLifshitz equation to an AC external field by performing a computation through the closed-form solution and the resulting hysteresis loop is displayed to show its deficiency. Then we modify the Landau-Lifshitz model into a new one by including a reversible part and an irreversible part accompanying with the switching criteria between these two states. With the new solutions we display the influence of parameters on the hysteresis loops of magnetic materials under AC fields. Keyword: Landau-Lifshitz equation, Magnetization, Hysteresis loop