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Theoretical Analysis of a Functionally Graded Shape Memory Alloy Beam under Pure Bending
No full textThe Functionally Graded Shape Memory Alloy (FG-SMA) is a new kind of functional materials which possesses the excellent properties of both Shape Memory Alloy (SMA) and Functionally Graded Material (FGM). A macro constitutive model of FG-SMA is established by using the theory of the mechanics of composites and the existing SMA model. With this macro constitutive model, the mechanical behavior of a FG-SMA beam composed by elastic material A and SMA subjected to pure bending is investigated. The loading processes including elastic process and phase transformation process are discussed in detail and the analytical solutions are obtained. What is more, a new layered method for establishing the finite element model of the FG-SMA beam is provided. The theoretical results show a good agreement with the experiment data, which indicates that the macro constitutive model and the finite element method provided here are valid. At last, the stress distribution on the cross section, the position of the neutral axis and the curvature-bending moment relation are discussed through numerical results, respectively. The obtained results demonstrate several interesting features of this new material, which may have potential applications in the future. This research can provide a base for the design and in-depth investigation of FG-SMA material
A Novel Meshless Analysis Procedure for Three-dimensional Structural Problems with Complicated Geometry
No full textA novel meshless analysis procedure is established for practical implementation in dealing with three-dimensional structures with complicated geometry. By this procedure, to describe the surface of structure, the Stereo-lithography (STL) geometry technique is first adopted. Nodes are then generated and paved uniformly in the space over the entire structure analyzed. To decide the node distribution inside the structure, a geometry-related treatment scheme with relevant checking mechanisms is developed. Besides, a simple and direct spatial integration scheme is also proposed. By this integration scheme, integration points are evenly distributed in the structure and can be adjusted easily to meet the required solution accuracy.
Two three-dimensional structural problems with irregular-shaped geometry are solved to demonstrate the advantages and high efficiency of the present novel meshless analysis procedure
Sample Size Dependence of Crack-tip Microstructure and Stress Evolutions in Single Crystal Nickel
No full textThe internal microstructure evolution and atomic stress distribution around the crack tip of a pre-cracked single crystal nickel with unequal sample sizes are studied by molecular dynamics (MD) simulation. The simulated results indicate that the crack propagation dynamics and stress distributions around the crack tip are strongly dependent on the microstructure evolution caused by the change of sample size. Unequal sample sizes induce various atomic configurations around the crack tip during the crack propagation. When atomic configuration is invariable around the crack tip, the crack grows rapidly along the crack path, the stress concentration occurs at the crack tip of growing crack and the stress is monotonic along the crack path. Once the occurrence of microstructure evolution (void nucleation, deformation twinning) around the crack tip, the crack grows slowly and the stress value is variable along the crack path due to the peak stress is accompanied by the appearance of the void and deformation twinning ahead of the crack tip. The pre-cracked single crystal nickel under mode I loading condition shows the different crack propagation dynamics and stress distribution, which are closely related to the sample size induces void nucleation and deformation twinning mechanisms around the crack tip
A Simple Proper Orthogonal Decomposition Method for von Karman Plate undergoing Supersonic Flow
Get PDFWe apply a simple proper orthogonal decomposition (POD) method to compute the nonlinear oscillations of a degenerate two-dimensional fluttering plate undergoing supersonic flow. First, the von Karman’s large deflection theory and quasi-steady aerodynamic theory are employed in constructing the governing equations of the simply supported plate. Then, the governing equations are solved by both the Galerkin method and the POD method. The Galerkin method is accurate but sometimes computationally expensive, since the number of degrees of freedom (dofs) required is relatively large provided that nonlinearity is strong. The POD method can be used to capture the complex dynamics of a strongly nonlinear system using very few degrees of freedom, much fewer than the Galerkin approach. The presently proposed POD method has two advantages over the conventional one. i) a simple numerical difference technique is first introduced to the POD method to avoid the complicated mode-to-mode projection between POD modes and Galerkin modes. ii) POD based reduced order models (POD/ROM) are constructed by using a set of general modes which is extracted from chaotic responses. That is to say POD modes extracted from one set of parameters can be applied to various parameter variations for the same dynamic system. Moveover, results for the buckled, LCO and chaotic responses of the plate are presented and compared with the Galerkin solutions. Numerical examples demonstrate the accuracy and efficiency of the present POD method
Using the Method of Fundamental Solutions for Obtaining Exponentially Convergent Helmholtz Eigensolutions
Get PDFIt is well known that the method of fundamental solutions (MFS) is a numerical method of exponential convergence. In this study, the exponential convergence of the MFS is demonstrated by obtaining the eigensolutions of the Helmholtz equation. In the solution procedure, the sought solution is approximated by a superposition of the Helmholtz fundamental solutions and a system matrix is resulted after imposing the boundary condition. A golden section determinant search method is applied to the matrix for finding exponentially convergent eigenfrequencies. In addition, the least-squares method of fundamental solutions is applied for solving the corresponding eigenfunctions. In the solution procedure, the sources of the MFS are located as far as possible and the precision saturation is avoided by using the multiple precision floating-point reliable (MPFR) library
Modeling and Simulation of Non-Newtonian Fluid Mold Filling Process with Phase Change
Get PDFA gas-liquid two-phase model for the simulation of a power-law fluid mold filling process with the consideration of phase change is proposed, in which the governing equations for the melt and air in the cavity, including the mass conservation, momentum conservation and energy conservation equations, are unified into one system of equation. A revised Enthalpy method, which can be used for both the melt and air in the mold cavity, is proposed to describe the phase change during the mold filling. Finite volume method on non-staggered grid is used to solve the system. The level set method is used to capture the interface evolution during the mold filling process. The interface evolution and the distributions of physical quantities such as velocity, pressure and temperature and so on are given. The “frozen skin” layers under different temperature and velocities conditions are discussed in detail. Numerical results show that increasing the temperatures of the melt and cavity is a better way to get rid of the “frozen skin” layer than increasing the injection velocity
On the Axisymmetric Time-harmonic Lamb’s Problem for a System Comprising a Half-space and a Covering Layer with Finite Initial Strains
Get PDFBy employing the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies (TLTEWISB) the time-harmonic Lamb’s problem for a system comprising a finite pre-strained half-space and finite pre-strained covering layer made of incompressible materials is examined for the case where the material of the covering layer is stiffer than that of the half-space material. It is assumed that on the upper free face plane of the covering layer the point-located time-harmonic force acts. The elasticity relations of the materials are described through Treloar’s potential. The corresponding boundary-value problem is solved by employing the Hankel integral transformation. The corresponding inverse transformations are found (numerically) by utilizing the Sommerfeld contour. Numerical results regarding the stresses acting on the interface plane are presented and discussed. The main focus is on the frequency response of these stresses and the influence of the initial strains on them. In particular, it is established that the mechanical behavior of the forced vibration of the system under consideration is similar to that of the system comprising a mass, a parallel connected spring and a dashpot. Moreover, it is established that by increasing the stiffness of the covering layer material as well as with initial stretching of the covering layer, the “resonance” values of the stresses decrease
Fuzzy Analysis of Structures with Imprecisely Defined Properties
Get PDFThis paper targets to analyse the static response of structures with fuzzy parameters using fuzzy finite element method. Here the material, geometrical properties and external load applied to the structures are taken as uncertain. Uncertainties presents in the parameters are modelled through convex normalised fuzzy sets. Fuzzy finite element method converts the problem into fuzzy or fully fuzzy system of linear equations for static analysis. As such here, two new methods are proposed to solve the fuzzy and fully fuzzy system of linear equations. Numerical examples for structures with uncertain system parameters that are in term of triangular fuzzy number are presented to illustrate the computational aspects of the proposed methods. The results obtained are depicted in term of plots
The time-dependent Green's function of the transverse vibration of a composite rectangular membrane
Get PDFA new method for the approximate computation of the time-dependent Green's function for the equations of the transverse vibration of a multi stepped membrane is suggested. This method is based on generalization of the Fourier series expansion method and consists of the following steps. The first step is finding eigenvalues and an orthogonal set of eigenfunctions corresponding to an ordinary differential operator with boundary and matching conditions. The second step is a regularization (approximation) of the Dirac delta function in the form of the Fourier series with a finite number of terms, using the orthogonal set of eigenfunctions. The third step is an approximate computation of the Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of eigenfunctions. The computational experiment confirms the robustness of the method
A Particle Simulation of 2-D Vessel Motions Interacting with Liquid-Sloshing Cargo
No full textThe violent free-surface motions interacting with floating vessels containing inner liquid tanks are investigated by using the newly developed Moving Particle Semi-implicit (MPS) method for 2-dimensional incompressible flow simulation. In the present numerical examples, many efficient and robust algorithms have been developed and applied to improve the overall quality and efficiency in solving various highly nonlinear free-surface problems and evaluating impact pressures compared to the original MPS method proposed by Koshizuka and Oka (1996). For illustration, the improved MPS method is applied to the simulation of nonlinear floating-body motions, violent sloshing motions and corresponding impact loads, and vessel motions with inner liquid tanks. It is seen that the roll amplitudes can be significantly reduced due to the presence of the sloshing tank when the excitation frequencies are away from the lowest sloshing natural frequencies. The developed numerical tools can be used to the study of vessel motions with liquid cargo or design of passive anti-rolling devices