جستجوی مقالات مرتبط با کلیدواژه « روش نیمه تحلیلی » در نشریات گروه « مکانیک »

The aim of the present paper is sensitivity of shape design analysis on thermo-elastic problems using a modified semi-analytical method. The semi-analytical method is one of the efficient methods for sensitivity analysis with respect to the design variables which combines the analytical method and finite difference method. Although this method is a powerful method, however, it is sensitive to perturbation size. Complex variables method is a new novel approach which is not sensitive to disturbance and has some potential advantages over other methods. The implementation of this method in a finite element code for sensitivities calculation is straightforward, only requiring a perturbation of the finite element mesh along the imaginary axis. This study uses the combination of analytical method and complex variables method to calculate the sensitivity of thermo-elastic problems. The proposed method has both advantages of the analytical method and the complex variables method. The advantages of this method are that it is quick, accurate and simple to implement. The obtained results are compared to other methods and it is shown that the proposed method is effective and can predict the stable and accurate sensitivity results.

The semi-analytical method (SAM) is an approach that computationally efficient and easy to implement. That's why this method often used for the sensitivity analysis of finite element models. However, SAM is not without defect especially in problems that rigid body motions are relatively large reveals severe inaccuracy. Such errors outcome from the pseudo load vector calculated by differentiation using the finite difference method. In the present paper, a new semi-analytical approach based on complex variables is proposed to compute the sensitivity of nonlinear finite element models. This method combines the complex variable method with the discrete sensitivity analysis to obtain the response sensitivity accurately and efficiently. The current approach maintains the computational efficiency of the semi-analytical method with higher accuracy. In addition, the current approach is insensitive to the choice of step size, a feature that simplifies its use in practical problems. The method can be used to nonlinear finite elements only requires minor modifications to existing finite element codes. In this paper, the authors demonstrate that the discrete sensitivity analysis and the complex variable method are equivalent and solve the same equation. Finally, the accuracy of the method is investigated through the various numerical examples by comparing by other methods and will show that this method is reliable and independent of step size.

In the present research, behavior of a sandwich plate with point supports subjected to an eccentric low-velocity impact is investigated. In this regard, time histories of the contact force and lateral deflection of a sandwich plate with simply supported edges are compared with those of a plate resting on point supports. This comparison has not been accomplished so far, even for the single-layer isotropic plates. Other novelty consists of proposing a semi-analytical solution in conjunction with a new energy formulation to consider the spatial dependency and using a numerical time integration method, implicitly. The governing equations of motions are found based on extremizing the total potential energy, including work of the inertia forces, employing Ritz technique and reduced to quasi-static one through a novel approach. In contrast to the available researches, influence of the lower layer on the stiffness of the contact region is incorporated. Verification of the results has been accomplished based on results of ABAQUS computer code. In the results section, the significant effects of the point supports (in comparison to the complete edge support), initial velocity of the indenter, and the aspect ratio of the plate on time histories of the contact force and lateral deflection of the plate are investigated.

In this research, modeling and vibrations analysis of the wind turbine blades and tower is studied. Modeling of each wind turbine blade is considered to be as elastic beam with rotational speed, and wind turbine tower is modeled as an Euler-Bernoulli elastic beam. Vibrations of blades and tower is considered in plane of rotation of blades. The equations of motion of the wind turbine are derived by Lagrangian approach and then numerically are solved. For the numerical solution, a limited number of elements are considered for the blades and the tower and then the natural frequencies of 2.5 MW SAMEN wind turbines is investigated by using its technical specifications. The effect of varying the length of the tower and the total mass of hub and nacelle on the natural frequencies is investigated, and the effect of varying the length of the blade on the natural frequencies of the blade is also investigated. Finally, the sensitivity analysis of the wind turbine natural frequencies with respect to different system parameters are presented.

In the present paper, buckling of multi-layer rectangular orthotropic composite plates with two longitudinal or transverse in-plane circular cutouts, on Winkler-Pasternak elastic foundation, is investigated. The analysis is accomplished through two steps. First, the in-plane pre-buckling stress components induced by the partial edge loads are determined and in the second stage, the Galerkin method is employed to develop the governing equations of the buckling. In this regard, the classical theory of plates, von Karman strain-displacement equations, Galerkin and energy approaches, and reduction of the problem to an eigenvalue problem are used. The buckling load is determined based on various relative locations of the cutouts and the: (1) uniform partial, (2) sinusoidal partial, and (3) concentrated edge loads, for the movable simply supported and clamped edge conditions. Furthermore, influence of the elastic foundation of the composite plate is investigated for different concentrated and partial loads. Results reveal that buckling of plates with holes or cutouts is dependent on opposite factors and may occur in local or global forms and the elastic foundation has pronounced effects of on the buckling load. This effect is more noticeable when the partial load is distributed on a larger length of the edge.

In this paper, vortex induced vibration of simply supported viscoelastic beam were investigated using semi-analytical method. By applying the general form of the viscoelastic model, the nonlinear partial differential equations of motion based on the Euler Bernoulli beam’s theory and displacement coupling fluid-structure interaction model were obtained via the Newton’s second law. A classical nonlinear van der Pol equation was taken as the governing equation for one component of the vortex shedding force on the beam. Employing the Galerkin discretization method, the equations of motion are reduced to a set of nonlinear ordinary differential equations with coupled terms and then there have been solved numerically by Runge-Kutta method. Finally, the effect of system parameters on the time response, phase plane and maximum amplitude of the beam are investigated. The results indicate that the viscoelastic behavior have a significant influence on the dynamic characteristics of the system and causes to change the Lock-in phenomenon with respect to corresponding elastic system. For example, for E2=10E1 the viscoelastic behavior can change the position of the locking area, and the maximum amplitude of the beam is increased by 45%. Lock-in from of vortex-induced vibrations was considered as a possible source of increased fatigue and damage. Therefore, by using viscoelastic materials the maximum amplitude of the system is reduced and the Lock-in condition can be changed. Additionally, based on the significant influence of viscoelastic behavior on the dynamic characteristics of the system, viscoelastic behavior should be considered in the mathematical model of the systems.

In this article, the free and forced convectional heat transfer in a rectangular porous fin with considering pressure loss across the fin length is investigated analytically. A well-known Differential transformation method is employed to obtain the solution of energy balance equation. Convergence of obtained solution is examined by previous works and they are found to be in a good agreement. In order to simulate heat transfer through porous media, Darcy model is applied. Also convective heat transfer coefficient is assumed to be constant. Dimensionless temperature distribution is defined as a function of convection and porosity parameters. Also the effects of pressure loss across the fin length on the temperature distribution, rate of heat transfer, fin efficiency and effectiveness of fin are studied. A comparative study is also made between the porous and solid fins for an equal mass of fins. It is highlighted that the porous fin transfer always more heat at specific condition compared to the solid fin. Results show that all of thermal parameters are influenced by pressure loss parameter. So in order to reach to high fin efficiency, pressure loss across the fin length should be controlled.

Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Within numerical design optimization, semi-analytical method for sensitivity analysis is frequently applied to estimate the derivative of an objective function with respect to the design variables. Generally numerical sensitivity analysis widely suffers from severe error due to the perturbation size and find a method which is not sensitive to the perturbation size is topics under study. Complex variable methods for sensitivity analysis have some potential advantages over other methods. For first order sensitivities using the complex variable method, the implementation is straightforward, only requiring a perturbation of the finite element mesh along the imaginary axis. This paper uses a complex variable and combine it with discrete sensitivity analysis, thus present new method to obtain derivatives for linear structure. The advantage of this method are quickly, accuracy and its simple implementation. The methodologies are demonstrated using two dimensional finite element models of linear elasticity problems with known analytical solutions. Obtained sensitivity derivatives are compared to the exact solution and also finite difference solutions and show that the proposed method is effective and can predict the stable and accurate sensitivity results.

In this research three-dimensional free vibration analysis of functionally graded circular plate with various boundary conditions is achieved. A semi-analytical method, which makes use of the state space method and the one-dimensional differential quadrature method, is used to obtain the vibration frequencies and dynamic responses of circular plates. Numerical results are given to demonstrate the accuracy and superiority of the presented method. The numerical results are compared with the existing numerical solutions and good agreement is displayed. Using the semi-analytical method, the analytical solution in the thickness direction is given and an effective approximate solution in the radial direction is obtained by selecting fewer discrete points.