A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded under Thermal and Mechanical Loadings

The constitutive relations and kinematic assumptions on the composite beam with shape memory alloy (SMA) arbitrarily embedded are discussed and the results related to the different kinematic assumptions are compared. As the approach of mechanics of materials is to study the composite beam with the SMA layer embedded, the kinematic assumption is vital. In this paper, we systematically study the kinematic assumptions influence on the composite beam deflection and vibration characteristics. Based on the different kinematic assumptions, the equations of equilibrium/motion are different. Here three widely used kinematic assumptions are presented and the equations of equilibrium/motion are derived accordingly. As the three kinematic assumptions change from the simple to the complex one, the governing equations evolve from the linear to the nonlinear ones. For the nonlinear equations of equilibrium, the numerical solution is obtained by using Galerkin discretization method and Newton-Rhapson iteration method. The analysis on the numerical difficulty of using Galerkin method on the post-buckling analysis is presented. For the post-buckling analysis, finite element method is applied to avoid the difficulty due to the singularity occurred in Galerkin method. The natural frequencies of the composite beam with the nonlinear governing equation, which are obtained by directly linearizing the equations and locally linearizing the equations around each equilibrium, are compared. The influences of the SMA layer thickness and the shift from neutral axis on the deflection, buckling and post-buckling are also investigated. This paper presents a very general way to treat thermo-mechanical properties of the composite beam with SMA arbitrarily embedded. The governing equations for each kinematic assumption consist of a third order and a fourth order differential equation with a total of seven boundary conditions. Some previous studies on the SMA layer either ignore the thermal constraint effect or implicitly assume that the SMA is symmetrically embedded. The composite beam with the SMA layer asymmetrically embedded is studied here, in which symmetric embedding is a special case. Based on the different kinematic assumptions, the results are different depending on the deflection magnitude because of the nonlinear hardening effect due to the (large) deflection. And this difference is systematically compared for both the deflection and the natural frequencies. For simple kinematic assumption, the governing equations are linear and analytical solution is available. But as the deflection increases to the large magnitude, the simple kinematic assumption does not really reflect the structural deflection and the complex one must be used. During the systematic comparison of computational results due to the different kinematic assumptions, the application range of the simple kinematic assumption is also evaluated. Besides the equilibrium study of the composite laminate with SMA embedded, the buckling, post-buckling, free and forced vibrations of the composite beam with the different configurations are also studied and compared.

Perturbational Finite Volume Method For The Solution of 2-D Navier-Stokes Equations on Unstructured and Structured Colocated Meshes

Based on the first-order upwind and second-order central type of finite volume( UFV and CFV) scheme, upwind and central type of perturbation finite volume ( UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from 0.3 to 0. 8 and convergence perform excellent with Reynolds number variation from 102 to 104.

Simulation of Free-Surface Flow in a Tank Using the Navier-Stokes Model and Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

High-Resolution Finite Compact Difference Schemes for Hyperbolic Conservation Laws

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknown variable for third-order FC-ENO scheme and two unknown variables for fifth-order FC-ENO scheme. Numerical test results of the proposed FC-scheme were compared with traditional TVD, ENO and WENO schemes to demonstrate its high-order accuracy and high-resolution.

A Crack Perpendicular to the Bimaterial Interface in Finite Solid

The dislocation simulation method is used in this paper to derive the basic equations for a crack perpendicular to the bimaterial interface in a finite solid. The complete solutions to the problem, including the T stress and the stress intensity factors are obtained. The stress field characteristics are investigated in detail. It is found that when the crack is within a weaker material, the stress intensity factor is smaller than that in a homogeneous material and it decreases when the distance between the crack tip and interface decreases. When the crack is within a stiffer material, the stress intensity factor is larger than that in a homogeneous material and it increases when the distance between the crack tip and interface decreases. In both cases, the stress intensity factor will increase when the ratio of the size of a sample to the crack length decreases. A comparison of stress intensity factors between a finite problem and an infinite problem has been given also. The stress distribution ahead of the crack tip, which is near the interface, is shown in details and the T stress effect is considered.

Determination of Proper Processing Conditions of Material Surface Heat Treatment Through Finite Element Method

A two-dimensional model has been developed based on the experimental results of stainless steel remelting with the laminar plasma technology to investigate the transient thermo-physical characteristics of the melt pool liquids. The influence of the temperature field, temperature gradient, solidification rate and cooling rate on the processing conditions has been investigated numerically. Not only have the appropriate processing conditions been determined according to the calculations, but also they have been predicted with a criterion established based on the concept of equivalent temperature area density (ETAD) that is actually a function of the processing parameters and material properties. The comparison between the resulting conditions shows that the ETAD method can better predict the optimum condition.

Relationships between hardness, elastic modulus, and the work of indentation

The work done during indentation is examined using dimensional analysis and finite element calculations for conical indentation in elastic-plastic solids with work hardening. An approximate relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work in indentation is found. Consequently, the ratio of hardness to elastic modulus may be obtained directly from measuring the work of indentation. Together with a well-known relationship between elastic modulus, initial unloading slope, and contact area, a new method is then suggested for estimating the hardness and modulus of solids using instrumented indentation with conical or pyramidal indenters.

Biosensor with Total Internal reflection Imaging Ellipsometry

In order to monitor multiple protein reaction processes simultaneously, a biosensor based on imaging ellipsometry operated in the total internal reflection mode is proposed. It could be realised as an automatic analysis for protein interaction processes with real-time label-free method. Its principle and methodology as well as a demonstration for its applications are presented.

A New Finite Element Method for Strain Gradient Theories and Applications to Fracture Analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J2 deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip.

Analysis of super compact finite difference method and application to simulation of vortex-shock interaction

Turbulence and aeroacoustic noise high-order accurate schemes are required, and preferred, for solving complex flow fields with multi-scale structures. In this paper a super compact finite difference method (SCFDM) is presented, the accuracy is analysed and the method is compared with a sixth-order traditional and compact finite difference approximation. The comparison shows that the sixth-order accurate super compact method has higher resolving efficiency. The sixth-order super compact method, with a three-stage Runge-Kutta method for approximation of the compressible Navier-Stokes equations, is used to solve the complex flow structures induced by vortex-shock interactions. The basic nature of the near-field sound generated by interaction is studied.

Evaluación de la sustitucion parcial o total de aceite de palma (Elaeis guinensis) por aceite de fritura como fuente de energía en la ración alimenticia de pollos de engorde

La presente investigación estuvo dirigida a determinar la viabilidad, que sobre el desempeño productivo del pollo de engorde, podía ejercer la sustitución parcial o total del porcentaje de aceite de palma (Elaeís guínensis, Jacq) por aceite de fritura como fuente de energía en la ración alimenticia. La sustitución parcial o total se hizo con base en el 6% de aceite que se incluye en la fórmula alimenticia, ajustada a los requerimientos de los pollos de engorde. El ensayo experimental fue realizado en la granja avícola "La Trinidad", propiedad de la empresa TIP-TOP INDUSTRIAL S.A. Se utilizaron 700 pollos de engorde para producción comercial, del híbrido Peterson-Hubbard, de un día de edad y mantenidos en evaluación durante un periodo de 42 días. Estos fueron distribuidos aleatoriamente en cuatro tratamientos, conformados cada uno de cinco unidades experimentales, y éstas a su vez con 35 pollos cada una, quedando de la forma siguiente: Tratamiento T1 (testigo): 6% aceite de palma; tratamiento T2 : 2% aceite de palma y 4% aceite de fritura; tratamiento T3: 1% aceite de palma y 5% aceite de fritura; tratamiento T4 : 6% aceite de fritura. El resto de los ingredientes que conformó la dieta alimenticia fue igual para todos los tratamientos; así como también el manejo de los pollos se realizó al igual que lo hace la Empresa para toda su producción. Las variables estudiadas fueron consumo de alimento, peso vivo final y conversión de alimento. Los resultados obtenidos a partir de estas variables fueron analizados a través de un Diseño Completamente Aleatorio y sometidos a la Prueba de Tukey, el que proporcionó la superioridad existente entre tratamientos. Se encontraron diferencias significativas (p<0.05) entre tratamientos para la variable conversión alimenticia, con índices de conversión para el final de período experimental, de 1.8050, 1.7829, 1.7550 y 1.7310 para los tratamientos T1, T2, T3 y T4, respectivamente. Las variables consumo acumulado de alimento y peso vivo final no presentaron diferencias estadísticas a un nivel de significancia de p<0.05. El análisis financiero demostró que el tratamiento T4 tiene un menor costo de alimentación, siendo este de C$3.35/kg peso vivo. Encontrándose los tratamientos T1.T2 y T3 con costos de C$3.8210, C$3.5624; y C$3.4527/kg peso vivo, respectivamente. El mayor beneficio neto por kilogramo de peso vivo lo obtuvo el tratamiento T4, con C$0.47. Siendo el beneficio neto para los tratamientos T2 y T3 de C$0.26 y C$ 0.37, respectivamente. La mortalidad presentada por los tratamientos T1, T2, T3, y T4 para el final del período experimental fue de 5.13, 3.99, 2.85 y 3.99 (%), respectivamente.

Efecto de distintos intervalos de mediciones de leche sobre la estimación de producción de leche total, repetibilidad y la forma de la curva de lactancia en un hato reyna

El presente trabajo se realizó con el objetivo de estudiar el efecto de cuatro intervalos de medición de leche (diario, cada 7, 14 y 28 días) sobre la producción de leche total, la repetibilidad y la forma de la curva de lactancia. Para lo cual se utilizaron los registros productivos y reproductivos del hato criollo Reyna de la Finca San José ubicada en Masatepe, Nicaragua. Se estudiaron 105 lactancia provenientes de 28 vacas durante el periodo de 1982 - 1990. Las características estudiadas fueron PLTOT, repetibilidad y la forma de la curva de lactancia. Todos los análisis estadísticos fueron realizados con el procedimiento de mínimos cuadrados y máxima verosimilitud establecido en el paquete estadístico LSMLMW total, obteniéndose las siguientes medias de mínimos cuadrados: 1,655.23±77.79 para el tratamiento 1 total. Los valores encontrados para los indices de Repetibilidad para cada uno de los tratamientos fueron de: 0.46±0.11, 0.50±0.11, 0.48±0.11 y 0.50±0.11 para los tratamientos 1, 2, 3, 4 respectivamente Los valores para los parámetros y variables estudias en la curva de la lactancia fueron 3.2±2.5, 0.47±0.32, 0.01± 0.06, 51.81±29.10, 9.45±3.49 y 6.97±1.02 para a, b, c, Tp, Rp y S respectivamente Al estudiar el efecto de los tratamiento sobre las variables y parámetros de la curva de lactancia se determino que solamente la variable (S) que determina la persistencia fue afectada significativamente

Distinct Element Analysis on Propagation Characteristics of P-Wave in Rock Pillar with Finite length

以节理岩体等效刚度的概念为基础,讨论了离散元刚性块体模型中节理刚度的选取问题。采用面-面接触模型模拟了纵波在一维岩体中的传播,给出了纵波波形；研究了阻尼比、软弱夹层以及节理间是否可拉对波传播规律的影响。

Hybrid Finite Compact-WENO Schemes for Shock Calculation

Hybrid finite compact (FC)-WENO schemes are proposed for shock calculations. The two sub-schemes (finite compact difference scheme and WENO scheme) are hybridized by means of the similar treatment as in ENO schemes. The hybrid schemes have the advantages of FC and WENO schemes. One is that they possess the merit of the finite compact difference scheme, which requires only bi-diagonal matrix inversion and can apply the known high-resolution flux to obtain high-performance numerical flux function; another is that they have the high-resolution property of WENO scheme for shock capturing. The numerical results show that FC-WENO schemes have better resolution properties than both FC-ENO schemes and WENO schemes. In addition, some comparisons of FC-ENO and artificial compression method (ACM) filter scheme of Yee et al. are also given.