Volume 22 (2017): Issue 1 (February 2017)

The purpose of this paper is to study the two dimensional deformation in a thermoelastic micropolar solid with cubic symmetry. A mechanical force is applied along the interface of a thermoelastic micropolar solid with cubic symmetry (Medium I) and a thermoelastic solid with microtemperatures (Medium II). The normal mode analysis has been applied to obtain the exact expressions for components of normal displacement, temperature distribution, normal force stress and tangential coupled stress for a thermoelastic micropolar solid with cubic symmetry. The effects of anisotropy, micropolarity and thermoelasticity on the above components have been depicted graphically.

The article presents an innovative use of inductive algorithm for generating the decision tree for an analysis of the rank validity parameters of construction and maintenance of the gear pump with undercut tooth. It is preventet an alternative way of generating sets of decisions and determining the hierarchy of decision variables to existing the methods of discrete optimization.

This paper is concerned with the problem of diffraction of an obliquely incident surface water wave train on an obstacle in the form of a finite step. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials are utilized to obtain a very accurate numerical estimate for reflection and transmission coefficients which are depicted graphically. From these figures various interesting results are discussed.

This paper provides a numerical analysis of selected parameters of fracture mechanics for double-edge notched specimens in tension, DEN(T), under plane strain conditions. The analysis was performed using the elastic-plastic material model. The study involved determining the stress distribution near the crack tip for both small and large deformations. The limit load solution was verified. The J-integral, the crack tip opening displacement, and the load line displacement were determined using the numerical method to propose the new hybrid solutions for calculating these parameters. The investigations also aimed to identify the influence of the plate geometry and the material characteristics on the parameters under consideration. This paper is a continuation of the author’s previous studies and simulations in the field of elastic-plastic fracture mechanics [4, 6, 16, 17, 31].

The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

The article presents a methodology of an analysis and modeling of technological systems and the grinding process of conical-like helical surfaces with the use of modern CAD/CAE systems and calculations in the Matlab system. The methodology developed allows one to carry out simulation tests for the accuracy of the grinding process of helical surfaces taking into consideration the deviations of the location and shape of the system’s elements, axial and radial striking the spindle of the workpiece machined and the grinding wheel as well as the tool’s geometrical features.

An exact solution of the combined study of Hall effects on a vertical plate with a rotating fluid in the presence of a homogeneous chemical reaction of first order has been analysed. The dimensionless governing coupled partial differential equations are tackled using the usual Laplace transform technique. The sway of the Hall parameter, Hartmann number, Grashof number, Prandtl number, Schmidt number, chemical reaction parameter on the axial velocity and concentration of the fluid has been depicted graphically. When the non-dimensional angular velocity, Ω=2M21+m.2$\Omega = {{{\it 2}M^2 } \over { {\it 1} + m.^{2} }}$, the transverse velocity component vanishes, thereby the axial velocity of the fluid attains the maximum value. It is noted that with increase in the Hall parameter, thermal Grashof number and mass Grashof number, the axial velocity of the fluid increases significantly.

The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux). The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM) and regular perturbation method (PM). The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM) and regular perturbation method (PM) methods shows the versatility of the Differential Transform Method (DTM). The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.

An unsteady magnetohydromagnetic natural convection on the Couette flow of electrically conducting water at 4°C (Pr = 11.40) in a rotating system has been considered. A Finite Element Method (FEM) was employed to find the numerical solutions of the dimensionless governing coupled boundary layer partial differential equations. The primary velocity, secondary velocity and temperature of water at 4°C as well as shear stresses and rate of heat transfer have been obtained for both ramped temperature and isothermal plates. The results are independent of the mesh (grid) size and the present numerical solutions through the Finite Element Method (FEM) are in good agreement with the existing analytical solutions by the Laplace Transform Technique (LTT). These are shown in tabular and graphical forms.

The fundamental equations of the two dimensional generalized thermoelasticity (L-S model) with one relaxation time parameter in orthotropic elastic slab has been considered under effect of rotation. The normal mode analysis is used to the basic equations of motion and heat conduction equation. Finally, the resulting equations are written in the form of a vector-matrix differential equation which is then solved by the eigenvalue approach. The field variables in the space time domain are obtained numerically. The results corresponding to the cases of conventional thermoelasticity CTE), extended thermoelasticity (ETE) and temperature rate dependent thermoelasticity (TRDTE) are compared by means of graphs.

The main aim of this paper is to present a Stochastic Finite Element Method analysis with reference to principal design parameters of bridges for pedestrians: eigenfrequency and deflection of bridge span. They are considered with respect to random thickness of plates in boxed-section bridge platform, Young modulus of structural steel and static load resulting from crowd of pedestrians. The influence of the quality of the numerical model in the context of traditional FEM is shown also on the example of a simple steel shield. Steel structures with random parameters are discretized in exactly the same way as for the needs of traditional Finite Element Method. Its probabilistic version is provided thanks to the Response Function Method, where several numerical tests with random parameter values varying around its mean value enable the determination of the structural response and, thanks to the Least Squares Method, its final probabilistic moments.

The global and local conditions of uniqueness and the criteria excluding a possibility of bifurcation of the equilibrium state for small strains are derived. The conditions and criteria are derived analyzing the problem of uniqueness of solution of the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This paper is a continuation of some previous works by the author, but contains new derivation of the global and local criteria excluding a possibility of bifurcation of the equilibrium state for a comparison body dependent on statically admissible fields of stress velocity. All the thermal elastoplastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem. The paper contains four Appendices A, B, C and D where the local necessery and sufficient conditions of uniqueness have been derived.

This paper presents an analysis of a parallelogram mechanism commonly used to provide a kinematic remote center of motion in surgical telemanipulators. Selected types of parallel manipulator designs, encountered in commercial and laboratory-made designs described in the medical robotics literature, will serve as the research material. Among other things, computer simulations in the ANSYS 13.0 CAD/CAE software environment, employing the finite element method, will be used. The kinematics of the solution of manipulator with the parallelogram mechanism will be determined in order to provide a more complete description. These results will form the basis for the decision regarding the possibility of applying a parallelogram mechanism in an original prototype of a telemanipulator arm.

This paper defines the design assumptions for the construction of an original demonstration of a CPM device, based on which a solid virtual model will be created in a CAD software environment. The overall dimensions and other input parameters for the design were determined for the entire patient population according to an anatomical atlas of human measures. The medical and physiotherapeutic community were also consulted with respect to the proposed engineering solutions. The virtual model of the CPM device that will be created will be used for computer simulations of changes in motion parameters as a function of time, accounting for loads and static states. The results obtained from computer simulation will be used to confirm the correctness of the design adopted assumptions and of the accepted structure of the CPM mechanism, and potentially to introduce necessary corrections. They will also provide a basis for the development of a control strategy for the laboratory prototype and for the selection of the strategy of the patient's rehabilitation in the future. This paper will be supplemented with identification of directions of further research.

The aim of this work is to study the mixed convection boundary layer flow from a horizontal surface embedded in a porous medium with exponential decaying internal heat generation (IHG). Boundary layer equations are reduced to two ordinary differential equations for the dimensionless stream function and temperature with two parameters: ε, the mixed convection parameter, and λ, the exponent of x. This problem is numerically solved with a system of parameters using built-in codes in Maple. The influences of these parameters on velocity and temperature profiles, and the Nusselt number, are thoroughly compared and discussed.