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Investigation on a Two-dimensional Generalized Thermal Shock Problem with Temperature-dependent Properties
Get PDFThe dynamic response of a two-dimensional generalized thermoelastic problem with temperature-dependent properties is investigated in the context of generalized thermoelasticity proposed by Lord and Shulman. The governing equations are formulated, and due to the nonlinearity and complexity of the governing equations resulted from the temperature-dependent properties, a numerical method, i.e., finite element method is adopted to solve such problem. By means of virtual displacement principle, the nonlinear finite element equations are derived. To demonstrate the solution process, a thermoelastic half-space subjected to a thermal shock on its bounding surface is considered in detail. The nonlinear finite element equations for this problem are solved directly in time domain. The variations of the considered variables are obtained and illustrated graphically. The results show that the effect of the temperature-dependent properties on the considered variables is to reduce their magnitudes, and taking the temperature-dependence of material properties into consideration in the investigation of generalized thermoelastic problem has practical meaning in predicting the thermoelastic behaviors accurately. It can also be deduced that directly solving the nonlinear finite element equations in time domain is a powerful method to deal with the thermoelastic problems with temperature-dependent properties
Numerical Solutions of Two-dimensional Stokes Flows by the Boundary Knot Method
Get PDFIn this paper, the boundary knot method (BKM) is adopted for accurately analyzing two-dimensional Stokes flows, dominated by viscous force and pressure gradient force. The Stokes flows, which denoted the flow fields with extremely viscous fluid or with very small velocity, appear in various engineering applications, such that it is very important to develop an efficient and accurate numerical method to solve the Stokes equations. The BKM, which can avoid the controversial fictitious boundary for sources, is an integral-free boundary-type meshless method and its solutions are expressed as linear combinations of nonsingular general solutions for Stokes equations. The weighting coefficients in the solution expressions can be acquired by enforcing the satisfactions of boundary conditions at every boundary node, since the non-singular general solutions are derived in this paper and already satisfied the Stokes equations. Three examples of two-dimensional Stokes flows were adopted to validate the accuracy and the simplicity of the BKM. Besides, the optimal shape parameter in the non-singular general solutions was determined by examining the minimum average residual of the linear system from the BKM
A High-Order Accurate Wavelet Method for Solving Three-Dimensional Poisson Problems
Get PDFBased on the approximation scheme for a L2-function defined on a three-dimensional bounded space by combining techniques of boundary extension and Coiflet-type wavelet expansion, a modified wavelet Galerkin method is proposed for solving three-dimensional Poisson problems with various boundary conditions. Such a wavelet-based solution procedure has been justified by solving five test examples. Numerical results demonstrate that the present wavelet method has an excellent numerical accuracy, a fast convergence rate, and a very good capability in handling complex boundary conditions
Comparison of Scenarios with and without Bridges and Analysis of Backwater Effect in 1-D and 2-D River Flood Modeling
Get PDFIn this paper the impact induced by bridges on the river flow is studied applying 1-D and 2-D unsteady flow models. Both the models are based on the Shallow Water Equations written in conservative form and solved with first order upwind schemes. In particular, the effect of bridges on the flow behavior simulated by the models is discussed from a practical point of view, with reference to the longitudinal and cross-section water surface profiles. Two cases characterized by bridges perpendicular to the principle flow direction are presented. The bridges are located in almost rectilinear river reaches whose cross-sections are confined by vertical artificial walls. Therefore, these cases represent typical situations for which 1-D approaches should be recommended. However, analysis of such results highlights two-dimensional features of the river flow that might influence the flood hazard assessment
Meshless Local Petrov-Galerkin and RBFs Collocation Methods for Solving 2D Fractional Klein-Kramers Dynamics Equation on Irregular Domains
No full textIn the current paper the two-dimensional time fractional Klein-Kramers equation which describes the subdiffusion in the presence of an external force field in phase space has been considered. The numerical solution of fractional Klein-Kramers equation is investigated. The proposed method is based on using finite difference scheme in time variable for obtaining a semi-discrete scheme. Also, to achieve a full discretization scheme, the Kansa's approach and meshless local Petrov-Galerkin technique are used to approximate the spatial derivatives. The meshless method has already proved successful in solving classic and fractional differential equations as well as for several other engineering and physical problems. The fractional derivative of equation is described in the Riemann-Liouville sense. In this paper we use a finite difference scheme to discretize the time fractional derivative of mentioned equation as the obtained scheme is of convergence order O(τ1+γ) for 0 < γ < 1. Also, we solve the mentioned equation on non-rectangular domains. The aim of this paper is to show that the meshless methods based on the strong form i.e. the radial basis functions collocation approach and local weak form i.e. meshless local Petrov-Galerkin idea are also suitable for the treatment of the fractional Klein-Kramers equation. Numerical examples confirm the high accuracy and acceptable results of proposed schemes
Research on Coal Pillar Width in Roadway Driving Along Goaf Based on The Stability of Key Block
No full textReasonable width design of narrow coal pillar is the key for ensuring stability of surrounding rock in the roadway driving along next goaf. Based on movement characteristics of overlying strata in gob-side entry, the paper establishes the mechanical model of surrounding rock structure for roadway driving along next goaf, and analyzes the interaction mechanism between key blocks and coal pillar. Besides, in allusion to the mechanical equilibrium of key block B in basic roof, the stability coefficients K1 and K2 of key block B and sensitive coefficient of influencing factor are introduced. When the stability coefficient K1 is larger than 1, rotation instability occurs; while the stability coefficient K2 is larger than 1, slip instability occurs. According to the stability analysis of key block B, the width design of coal pillar in roadway driving along goaf is obtained. By taking No.3307 working face in Xinan coal mine in Shandong Province as project background, the paper determines reasonable width of coal pillar, calculates stability coefficients of key blocks, and obtains sensitive coefficients of influencing factors on the stability of key blocks. The practical results indicate that the stability of key block in roadway driving along next goaf can be guaranteed when the width of coal narrow is 5.0 m. The results can provide theoretical basis and technical guidance for engineering application with similar mining conditions
Dynamic Instability of Straight Bars Subjected to Impulsive Axial Loads Using the DEM
Get PDFSince the half of the XX century, attention was given to the instability of structures under parametric excitation, especially under periodic loads. On the other hand, the instability of bars subjected to axial loads of impulsive type has been little studied, in spite of the practical importance of the topic. Thus, in Engineering Design it is frequently supposed, without tests or additional verifications, that an axial load of short duration can exceed the Euler critical load of the bar without inducing damage in the same.
Within this context, this paper proposes the use of the truss-like Discrete Element Method (DEM) for determining the dynamic response of elastic straight bars subjected to axial loads defined by pulses of short duration. The proposed approach allows the consideration of initial imperfections, as well as large displacements and other non-linear effects. The influence of the pulse duration and other effects in the response of the bar are also evaluated. Initially, the performance of the proposed methodology is verified in static and dynamic instability problems of homogeneous bars without geometrical imperfections, by comparing the DEM results with analytical solutions available in the literature. After that, the DEM is employed to analyze more complex cases, including bars with initial imperfections and non-homogeneous bars, in which material properties, as Young’s modulus and mass density, are assumed to be correlated Gaussian random fields. The proposed methodology has proven to be a useful and easy tool for analysis of dynamic instability of bars and could therefore be used by designers for estimating the dynamic buckling load
Trans-scale Granular Modelling of Cytoskeleton: a Mini-Review
Get PDFLiving cells are the functional unit of organs that controls reactions to their exterior. However, the mechanics of living cells can be difficult to characterize due to the crypticity of their microscale structures and associated dynamic cellular processes. Fortunately, multiscale modelling provides a powerful simulation tool that can be used to study the mechanical properties of these soft hierarchical, biological systems. This paper reviews recent developments in hierarchical multiscale modeling technique that aimed at understanding cytoskeleton mechanics. Discussions are expanded with respects to cytoskeletal components including: intermediate filaments, microtubules and microfilament networks. The mechanical performance of difference cytoskeleton components are discussed with respect to their structural and material properties. Explicit granular simulation methods are adopted with different coarse-grained strategies for these cytoskeleton components and the simulation details are introduced in this review
A Coupled Mathematical Model of Cell Migration, Vessel Cooption and Tumour Microenvironment during the Initiation of Micrometastases
Get PDFWe propose a coupled mathematical model for the detailed quantitative analyses of initial microtumour and micrometastases formation by including cancer cell migration, host vessel cooption and changes in microenvironment. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. Migration probability of a migrating cell is assumed to be influenced by local chemical microenvironment. Pre-existing vessel cooption and remodelling are introduced according to the local haemodynamical microenvironment, such as interstitial pressure and vessel wall permeability. After the tumour cells and tumour vessels distribution are updated, the chemical substances are coupled calculated with the haemodynamical environment. The simulation results clearly reproduce the tumour cells migrate and proliferate along the pre-existing vessels at the very early stage of growth, which are consistent with many published experimental observations. In addition, the model demonstrates the interactions of tumour cells with the pre-existing vessels, which are believed to be essential for initial adhesion, proliferation, invasion, and micrometastases establishment. Quantitative analysis of tumour expansion in longitudinal and transverse directions shows that the cooption and migration along host vessels will be inhibited once angiogenesis phase occurs. The influences of the ability of cell migration and the inclusion of vessel cooption on the formation of micrometastases are discussed
Exact Solutions for the Stability and Free Vibration of Multilayered Functionally Graded Material Hollow Cylinders under Axial Compression
Get PDFExact three-dimensional stability and free vibration analyses of simply-supported, multilayered functionally graded material (FGM) circular hollow cylinders and laminated composite ones under axial compression are presented. The material properties of each FGM layer are assumed to obey a power-law distribution of the volume fractions of constituents through the thickness coordinate. The Pagano method, which is based on the principle of virtual displacement and is conventionally used for the analysis of laminated composite structures, is modified to be feasible for the study of multilayered FGM cylinders, in which Reissner's mixed variational theorem, the successive approximation and transfer matrix methods, and the transformed real-valued solutions of the system equations are used. The present modified Pagano solutions for laminated composite cylinders are in excellent agreement with the exact 3D ones available in the literature, and those for sandwich FGM cylinders may be used as the benchmark solutions to assess the ones obtained using various two-dimensional theories and numerical models. The influence of some effects on the lowest critical load parameters of multilayered FGM cylinders and laminated composite ones is investigated, such as the derivation between using von Karman nonlinearity and full kinematic one, and the difference between using the uniform stress assumption and the uniform strain one. In addition, a parametric study with regard to some effects on the lowest frequency parameters of axially loaded, multilayered FGM cylinders is carried out, such as the magnitude of the applied compressive loads, the radius-to-thickness, length-to-radius and orthotropic ratios, and the material-property gradient index