• Structural Engineering and Mechanics
• /
• v.24 no.2
• /
• pp.227-245
• /
• 2006

The performance of a three dimensional non-linear finite element model for hyperelastic material considering the effect of compressibility is studied by analyzing rubber blocks under different modes of deformation. It includes simple tension, pure shear, simple shear, pure bending and a mixed mode combining compression, shear and bending. The compressibility of the hyperelastic material is represented in the strain energy function. The nonlinear formulation is based on updated Lagrangian (UL) technique. The displacement model is implemented with a twenty node brick element having u, ${\nu}$ and w as the degrees of freedom at each node. The results obtained by the present numerical model are compared with the analytical solutions available for the basic modes of deformation where the agreement between the results is found to be satisfactory. In this context some new results are generated for future references since the number of available results on the present problem is not sufficient enough.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.22 no.1
• /
• pp.45-49
• /
• 2013

It is important to have a well developed strain energy function in order to understand the mechanical behavior of biomaterial like the blood vessel of artery. However, since it is not possible to have a complete form of strain energy function of artery, theoretical framework describing the behaviour of Rubber-like material which is similar to blood vessel is applied to infer useful forms of strain energy function of biomaterial. Based on Chuong-Fung model and Mooney-Rivlin model, material parameters are estimated based on experimental data. From the results, it can be inferred that the estimated parameters can be used to explain the difference of mechanical characteristics between normal vessel and vessel with stent.

• Smart Structures and Systems
• /
• v.8 no.5
• /
• pp.433-447
• /
• 2011

The present paper addresses the nonlinear response of a FG square plate with two smart layers as a sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect to amplitude of displacements and electrical potential. The effect of non homogenous index was investigated on the responses of the system. Obtained results indicate that with increasing the non homogenous index, the displacements and electric potential tend to an asymptotic value. Displacements and electric potential can be presented in terms of planar coordinate system. A linear analysis was employed and then the achieved results are compared with those results that are obtained using the nonlinear analysis. The effect of the geometric nonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis. Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can be presented as novelty of this study.

• Smart Structures and Systems
• /
• v.5 no.1
• /
• pp.23-42
• /
• 2009

In order to reduce vibration or to control shape of structures made of metal or composites, piezoelectric materials have been extensively used since their discovery in 1880's. A recent trend is also seen to apply piezoelectric materials to flexible structures made of rubber-like materials. In this paper a non-linear finite element model using updated Lagrangian (UL) approach has been developed for static analysis of rubber-elastic material with surface-bonded piezoelectric patches. A compressible stain energy function has been used for modeling the rubber as hyperelastic material. For formulation of the nonlinear finite element model a twenty-node brick element is used. Four degrees of freedom u, v and w and electrical potential ${\varphi}$ per node are considered as the field variables. PVDF (polyvinylidene fluoride) patches are applied as sensors/actuators or sensors and actuators. The present model has been applied to bimorph PVDF cantilever beam to validate the formulation. It is then applied to study the smart rubber components under different boundary and loading conditions. The results predicted by the present formulation are compared with the analytical solutions as well as the available published results. Some results are given as new ones as no published solutions available in the literatures to the best of the authors' knowledge.

• Journal of Mechanical Science and Technology
• /
• v.17 no.10
• /
• pp.1496-1506
• /
• 2003

The SIMP (solid isotropic material with penalization) approach is perhaps the most popular density variable relaxation method in topology optimization. This method has been very successful in many applications, but the optimization solution convergence can be improved when new variables, not the direct density variables, are used as the design variables. In this work, we newly propose S-shape functions mapping the original density variables nonlinearly to new design variables. The main role of S-shape function is to push intermediate densities to either lower or upper bounds. In particular, this method works well with nonlinear mathematical programming methods. A method of feasible directions is chosen as a nonlinear mathematical programming method in order to show the effects of the S-shape scaling function on the solution convergence.

• International Journal of Control, Automation, and Systems
• /
• v.4 no.2
• /
• pp.178-186
• /
• 2006

We propose and analyze a robust adaptive fuzzy controller for nonlinear systems without a priori knowledge of the sign of the input gain function. No assumptions are made about the type of nonlinearities of the system, except that such nonlinearities are smooth. The uncertain nonlinearities are captured by the fuzzy systems that have been proven to be universal approximators. The proposed control scheme completely overcomes the singularity problem that occurs in the indirect adaptive feedback linearizing control. Projection in the estimated parameters and switching in the control input are both not required. The stability of the closed-loop system is guaranteed in the Lyapunov viewpoint.

• Journal of Korean Society of Steel Construction
• /
• v.11 no.4 s.41
• /
• pp.417-424
• /
• 1999

In this paper a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity includes gradual yielding associated with flexural behaviors. The geometric nonlinearity includes the second-order effects associated with $P-{\delta}\;and\;P-{\Delta}$ effects. The material nonlinearity at the node is considered using the concept of P-M hinge consisting of many fibers. The geometric nonlinearity is considered by the use of stability function. The nonlinearity caused by shear and torsional interaction effects is neglected. The modified incremental displacement method is used as the solution technique. The load-displacements predicted by the proposed analysis compare well with those given by other approaches.

• Nuclear Engineering and Technology
• /
• v.53 no.9
• /
• pp.3100-3111
• /
• 2021

Numerical modeling for the safety-related equipment used in a nuclear power plant (i.e., cabinet facilities) plays an essential role in seismic risk assessment. A full finite element model is often time-consuming for nonlinear time history analysis due to its computational modeling complexity. Thus, this study aims to generate a simplified model that can capture the nonlinear behavior of the electrical cabinet. Accordingly, the distributed plasticity approach was utilized to examine the stiffness-degradation effect caused by the local buckling of the structure. The inherent dynamic characteristics of the numerical model were validated against the experimental test. The outcomes indicate that the proposed model can adequately represent the significant behavior of the structure, and it is preferred in practice to perform the nonlinear analysis of the cabinet. Further investigations were carried out to evaluate the seismic behavior of the cabinet under the influence of the constitutive law of material models. Three available models in OpenSees (i.e., linear, bilinear, and Giuffre-Menegotto-Pinto (GMP) model) were considered to provide an enhanced understating of the seismic responses of the cabinet. It was found that the material nonlinearity, which is the function of its smoothness, is the most effective parameter for the structural analysis of the cabinet. Also, it showed that implementing nonlinear models reduces the seismic response of the cabinet considerably in comparison with the linear model.

• Structural Engineering and Mechanics
• /
• v.75 no.6
• /
• pp.701-711
• /
• 2020

This papers studies nonlinear stability and post-buckling behaviors of geometrically imperfect metal foam doubly-curved shells with eccentrically stiffeners resting on elastic foundation. Metal foam is considered as porous material with uniform and non-uniform models. The doubly-curved porous shell is subjected to in-plane compressive loads as well as a transverse pressure leading to post-critical stability in nonlinear regime. The nonlinear governing equations are analytically solved with the help of Airy stress function to obtain the post-buckling load-deflection curves of the geometrically imperfect metal foam doubly-curved shell. Obtained results indicate the significance of porosity distribution, geometrical imperfection, foundation factors, stiffeners and geometrical parameters on post-buckling characteristics of porous doubly-curved shells.

• Elastomers and Composites
• /
• v.37 no.3
• /
• pp.151-158
• /
• 2002

An elastomeric bushing which has been considered in this research is a device used in automotive suspension systems to reduce the forte transmitted iron the wheel to the frame of the vehicle. A bushing is modeled at a hollow cylinder which is bonded to a solid metal shaft at its inner surface and a metal sleeve at its outer surface. Lianis constitutive equation for a nonlinear viscoelastic incompressible material is used to model the elastomeric material of the bushing. It is used to derive a force-displacement relation for axial response of the bushing. The displacement dependent force relaxation function for the bushing is obtained from the ramp displacement control tests with an extrapolation method. This is compared with the exact result obtained from the step displacement control test and the results are in very good agreement.