Sharif Digital Repository

A local radial basis function (RBF) meshless method is applied for solution of the Burgers' equation with different initial and boundary conditions of various complexities. Local-RBF collocation is employed for discretization in space, whilst the unsteady term is handled via a simple explicit time discretization. Moreover, in case of non-smooth initial conditions with high Reynolds numbers, a treatment is proposed for inability of local-RBF methods to solve such problems. The scheme is validated over a variety of benchmark problems and very good agreement is found with existing analytical and numerical solutions  

An enhanced unfolding inverse finite element method (IFEM) is used together with an extended strain-based forming limit diagram (EFLD) to develop a fast and reliable approach to predict the feasibility of the deep drawing process of a part and determining where the failure or defects can occur. In the developed unfolding IFEM, the meshed part is properly fold out on the flat sheet and treated as a 2D problem to reduce the computation time. The large deformation relations, nonlinear material behavior and friction conditions in the blank holder zone are also considered to improve the accuracy and capability of the proposed IFEM. The extended strain-based forming limit diagram based on the... 

The forming limit stress diagram (FLSD) has been reported as being much less path dependent and much more favourable than the forming limit diagram (FLD) in representing forming limits in the numerical simulation of sheet metal forming processes. Therefore, the purpose of this study was to develop a methodology for the prediction of the forming limits both in strain and stress forms. All simulations are based on strain gradient theory of plasticity in conjunction with the Marciniak-Kuczynski (M-K) approach. This approach introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation inhomogeneity and material softening. The... 

Presented within this paper is the identification of impact force acting on a simply supported beam. The force identification is an inverse problem in which the measured response of the structure is used to determine the applied force. The identification problem is formulated as an optimization problem and genetic algorithm is utilized to solve the optimization problem. The objective function is calculated on the difference between analytical and measured responses and the decision variables are the location and magnitude of the applied force. The results from simulation show the effectiveness of the approach and its robustness to the measurement noise and sensor location  

An exact planar solution for the determination of electroelastic responses are presented for functionally graded piezoelectricmaterials (FGPMs). The electro-mechanical properties are assumed to vary exponentially. Exploiting the potential functions for stress and induction, the governing equations reduce to systems of fourth order inhomogeneous partial differential equations (PDEs), which are solved in a closed form manner. Validity of the obtained solution is checked by other existing results in the literatures. Several examples are provided under distinctive thermo-electro-mechanical loadings. Finally, the effect of the graded indices is examined upon the electroelastic response of the FGP... 

In this study, an analytical solution is presented for thermo-electro- elastic analysis of piezoelectric semi-infinite bodies. For this purpose, governing equations are derived for a transversely isotropic piezoelectric material under an axisymmetric thermo-electro-mechanical loading condition. A general closed-form analytical solution is presented for the complementary and particular parts of the components of the displacement vector and also for the electric potential function. Then, boundary conditions are imposed and in that case an explicit solution is obtained for piezoelectric semi-infinite bodies. Results show that when a piezoelectric half space is subjected to constant/ramp surface... 

The present paper addresses an analytical method to determine the electroelastic fields over a double-phase piezoelectric reinforcement interacting with an ellipsoidal single-inhomogeneity. The approach is based on the extension of the electro-mechanical equivalent inclusion method (EMEIM) to the piezoelectric double-inhomogeneity system. Accordingly, the double-inhomogeneity is replaced by an electroelastic double-inclusion problem with proper polynomial eigenstrains-electric fields. The long- and short-range interaction effects are intrinsically incorporated by the homogenizing eigenfields. The equivalent double-inclusion is subsequently decomposed to the single-inclusion problems by means... 

Consider two piezoelectric ellipsoidal inhomogeneities of arbitrary size, orientation and material constants, which in turn are surrounded by an infinite isotropic medium. The system under consideration is subjected to far-field non-uniform electromechanical loadings. Based on the extension of the electromechanical equivalent inclusion method (EMEIM), the present paper develops a unified solution for determination of the associated electroelastic fields in the vicinity of interacting inhomogeneities. Accordingly, each of the piezoelectric inhomogeneities is broken down into two equivalent inclusions with proper polynomial eigenstrains and eigenelectric fields. The robustness and efficacy of... 

In this work, the formability of a hybrid material of Interstitial-Free 240 (IF240) steel and AZ31 magnesium alloy as IF240/AZ31/IF240 tri-layered sheets was investigated. For this purpose, the bonding feasibility of the high-formability IF240 steel and low-formability AZ31 sheets was first assessed. Then, the hot formability behavior of the manufactured laminated composite was evaluated. The rolling of the preheated samples established the layer bonding. The bonding strength was determined using the shear punch test. The texture and its effects on the forming behavior were studied using the x-ray Goniometry method. Nakazima dome tests were employed at ambient and elevated temperatures to... 

In this work, the formability of a hybrid material of Interstitial-Free 240 (IF240) steel and AZ31 magnesium alloy as IF240/AZ31/IF240 tri-layered sheets was investigated. For this purpose, the bonding feasibility of the high-formability IF240 steel and low-formability AZ31 sheets was first assessed. Then, the hot formability behavior of the manufactured laminated composite was evaluated. The rolling of the preheated samples established the layer bonding. The bonding strength was determined using the shear punch test. The texture and its effects on the forming behavior were studied using the x-ray Goniometry method. Nakazima dome tests were employed at ambient and elevated temperatures to... 

The electroelastic response of functionally graded piezoelectric cantilever beams which includes the effect of body force is presented in this paper. The material properties such as elastic compliance, piezoelectric and dielectric impermeability are assumed to be graded with different indices in the thickness direction according to exponential distributions. Systems of fourth order inhomogeneous partial differential equations (PDEs) which are satisfied by the stress and induction functions and involve the body force terms are derived. Spectral forms for electrical and mechanical variables in the x-axis are employed to convert the partial differential governing equations and the associated... 

Consider an arbitrarily oriented ellipsoidal domain near the interface of an isotropic bimaterial space. It is assumed that a general class of piecewise nonuniform dilatational eigenstrain field is distributed within the ellipsoidal domain. Two theorems relevant to prediction of the nature of the induced displacement field for the interior and exterior points of the ellipsoidal domain are stated and proved. As a resultant the exact analytical expression of the elastic fields are obtained rigorously. In this work a new Eshelby-like tensor, A is introduced. In particular, the closed-form expressions for A associated with the interior points of spherical and cylindrical inclusion are derived.... 

In the present study, a special heat treatment cycle (step quenching) was used to produce a dual-phase (DP) microstructure in low carbon steel. By producing this DP microstructure, the mechanical properties of the investigated steel such as yield stress, tensile strength, and Vickers hardness were increased 14, 55, and 38%, respectively. In order to investigate the effect of heat treatment on formability of the steel, Nakazima forming test was applied and subsequently finite element base modeling was used to predict the outcome on forming limit diagrams. The results show that the DP microstructure also has a positive effect on formability. The results of finite element simulations are in a... 

A theoretical forming limit stress diagram (FLSD) for necking prediction which is based on the strain gradient theory of plasticity in conjunction with the M-K approach was represented and used in tube hydroforming. This approach introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation inhomogeneity and material softening. The nonlinear second order ordinary differential equation of the thickness of tube has been solved by collocation method. It has been shown that this method overcomes the imperfection sensitivity encountered in the conventional M-K method. The predicted FLSD has been compared with published experimental... 

Forming limit diagram is often used as a criterion to predict necking initiation in sheet metal forming processes. In this study, the forming limit diagram was obtained through the inclusion of the Marciniak–Kaczynski model in the Nakazima out-of-plane test finite element model and also a flat model. The effect of bending on the forming limit diagram was investigated numerically and experimentally. Data required for this simulation were determined through a simple tension test in three directions. After comparing the results of the flat and Nakazima finite element models with the experimental results, the forming limit diagram computed by the Nakazima finite element model was more convenient... 

In this study, the mechanical properties, formability and forming limit diagrams (FLDs) of the tailor-welded blanks (TWBs) produced by friction stir welding (FSW) were analyzed experimentally. At first, the suitable FSW parameters were achieved. The formability and FLDs of TWBs were evaluated for sheets with the same or different thicknesses and compared to the base metal sheet. This study was performed on low carbon steel (St14) sheets with a lot of applications in automobile industries. The welded zone properties were evaluated by some experiments. The tensile test, micro hardness testing, and metallographic studies were done. The effect of welding seam directions on formability and FLD... 

In this study, the effect of through-thickness shear (TTS) stress has been examined on the prediction of forming limit diagrams (FLDs). Determination of the FLD is based on the Marciniak–Kuczynski (M–K) model with some modifications on the stress states for consideration of the TTS stress effects. For solving the equations, the Newton–Raphson method has been used. Furthermore, the Nakazima test has been simulated to investigate the stress state which occurs in the sheet during the test. Results showed that the formability of sheet metal could be better as the through-thickness stress increased. Also, implementation of TTS stress in the present model, the corresponding FLD has better... 

In this article, we investigated the effect of martensite morphology on the mechanical properties and formability of dual phase steels. At first, three heat treatment cycles were subjected to a low-carbon steel to produce ferrite–martensite microstructure with martensite morphology of blocky-shaped, continuous, and fibrous. Tensile tests were then carried out so as to study mechanical properties, particularly the strength and strain hardening behavior of dual phase steels. In order to study the formability of dual phase samples, Forming Limit Diagram was obtained experimentally and numerically. Experimental forming limit diagram was obtained using Nakazima forming test, while Finite Element... 

In this study, the effect of through-thickness shear (TTS) stress has been examined on the prediction of forming limit diagrams (FLDs). Determination of the FLD is based on the Marciniak–Kuczynski (M–K) model with some modifications on the stress states for consideration of the TTS stress effects. For solving the equations, the Newton–Raphson method has been used. Furthermore, the Nakazima test has been simulated to investigate the stress state which occurs in the sheet during the test. Results showed that the formability of sheet metal could be better as the through-thickness stress increased. Also, implementation of TTS stress in the present model, the corresponding FLD has better...