Computational Methods in Engineering

In this research, nonlinear dynamic analysis of concrete shear wall using a new nonlinear model based on damage mechanics approach and considering bond slip effects is presented. Nonlinear behavior of concrete is modeled by a rotational smeared crack model using damage mechanics approach. The proposed model considers major characteristics of the concrete subjected to two and three dimensional loading conditions. These characteristics are pre-softening behavior, softening initiation criteria and fracture energy conservation. The model was used in current research analysis after verification by some available numerical tests. Reinforcements are modeled by a bilinear relationship using two models: Discrete truss steel element and Smeared model. In Discrete model the effects of bond-slide between concrete and rebar is mentioned using the bond-link element model concept. Based on the presented algorithms and methodology, an FEM code is developed in FORTRAN. The validity of the proposed models and numerical algorithms has been checked using the available experimental results. Finally, numerical simulation of CAMUS I and CAMUS III reinforced concrete shear walls is carried out. Comparisons of deduced results confirm the validity of proposed models. The obtained results, both in the expected displacements and crack profiles for the walls, show a good accuracy with respect to the experimental results. Also, using discrete truss element model with respect to the smeared steel model leads to increasing the accuracy of maximum displacement response to 7% in analysis.

Since there is no closed-form formula for designing TMD (Tuned Mass Damper) for nonlinear structures, some researchers have proposed numerical optimization procedures such as a genetic algorithm to obtain the optimal values of TMD parameters for nonlinear structures. These methods are based on determining the optimal values of TMD parameters to minimize the maximum response (e.g. inter story drift) of the controlled structure subjected to a specific earthquake record. Therefore, the performance of TMD that has been designed using a specific record strongly depends on the characteristics of the earthquake record. By changing the characteristics of the input earthquake record, the efficiency of TMD is changed and in some cases, it is possible that the response of the controlled structure is increased. To overcome the shortcomings of the previous researches, in this paper, an efficient method for designing optimal TMD on nonlinear structures is proposed, in which the effect of different ground motion records is considered in the design procedure. In the proposed method, the optimal value of the TMD parameters are determined so that the average maximum response (e.g. inter story drift) resulting from different records in the controlled structure is minimized. To illustrate the procedure of the propose method, the method is used to design optimal TMD for a sample structure. The results of numerical simulations show that the average maximum response of controlled structure resulting from different records is reduced significantly. Hence, it can be concluded that the proposed method for designing optimal TMD under different earthquakes is effective.

In this research, a new method called elastic surface algorithm is presented for inverse design of 2-D airfoil in a viscous flow regime. In this method as an iterative one, airfoil walls are considered as flexible curved beams. The difference between the target and the current pressure distribution causes the flexible beams to deflect at each shape modification step. In modification shape algorithm, the finite element equations of two-node Timoshenko beam are solved to calculate the deflection of the beams. In order to validate the proposed method, various airfoils in subsonic and transonic regimes are studied, which show the robustness of the method in the viscous flow regime with separation and normal shock. Also, three design examples are presented here, which show the capability of the proposed method.

In this paper, considering all the linear and nonlinear inertia terms of moving masses on a flexible beam, the dynamic response and dynamic stability of the beam are studied. Homotopy perturbation method is used to perform the analysis and results are provided in a stability map for the different values of mass and velocity of the moving masses. It is concluded that there is a borderline in the diagram that separates the stable and unstable regions. For the first time, this borderline is determined semi-analytically. Results of the stability analysis are validated using the Floquet theory. In addition to this borderline, it is also concluded that the Homotopy perturbation method is capable of evaluating the new critical values for mass and velocity which cause vibration resonance in the beam. The locus of these resonant points, which is totally a new finding in dynamic analysis of beam-moving mass problem, is determined semi-analytically. Finally, the effect of the friction between the beam and the moving mass is studied on the stability of the system and resonant conditions. Accuracy of the results for this case is also evaluated with a numerical simulation.

In this study, for the first time, a comparison of single-relaxation-time, multi-relaxation-time and entropic lattice Boltzmann methods on non-uniform meshes is performed and application of these methods for simulation of two-dimensional cavity flows, channel flows and channel flows with sudden expansion is studied in the slip and near transition regimes. In this work, Taylor series expansion and least squares based lattice Boltzmann method is utilized in order to apply the lattice Boltzmann models on non-uniform meshes. A diffuse scattering boundary condition and a combination of bounce-back and specular boundary conditions are employed to obtain the slip at the walls. Besides, the relaxation times of lattice Boltzmann methods are computed in terms of Knudsen number. Different lattice Boltzmann methods are used to simulate lid-driven micro cavity flows and their results are compared with each other and with those obtained in the literature. Then, the best model in accuracy and stability, i.e. multi-relaxation-time lattice Boltzmann method, is applied to simulate the micro channel flow in different Knudsen numbers. Results show that the proposed method on non-uniform meshes is capable of simulating micro flows problems in the slip and the transition regimes.

In this paper,  a numerical model  was first verified against dynamic centrifuge tests results performed on an
underground subway tunnel and then, the effect of underground structure on peak ground acceleration (PGA) at the ground
surface investigated considering linear and nonlinear behavior for the soil. The results show that in the range of natural
frequency of the system, nonlinear model shows deamplification of PGA with respected to the freefield. Whereas, linear model
shows opposite trend. Out of the range of natural frequency of the system, linear and nonlinear models predict same results and for both model, underground tunnel resulted in amplification of  low frequencies and deamplification of high frequencies with
respected to the freefield.

In this paper, a new vibration-based damage detection method for damage localization in shear frames is presented. For this purpose, a new damage index is proposed by means of static displacements estimated using only the first several mode data and Grey Relation Theory. The efficiency of the presented method has been demonstrated through studying several damage scenarios on three examples of shear frames with a different number of stories. The effects of various situations such as the existence random noises in the recorded data, number of available modes, different damage scenarios and irregularity in the structural characteristics have been studied on the applicability of the presented method. The obtained results show the robustness and good performance of the presented method in the damage diagnosis of shear frames. Some of the most important advantages of the suggested method can be summarized as its ability in damage localization by means of only the first mode data, low sensitivity to the random noises, and high speed and accuracy in estimating damage locations.

Buckling under compression is a common phenomenon for thin-walled structures. Under certain conditions, they can also buckle locally under tensile loads. In this paper, the buckling of cracked panels is investigated. Effects of some parameters such as the length and orientation of crack, length, width and thickness of the panel and boundary conditions on the compressive and tensile buckling loads are determined. The results show that the dimensions of panels have the least and characteristics of crack have the most effect on the buckling.

The phase transformation phenomenon due to the crystallographic change of shape memory alloys subjected to mechanical or thermal loading is very complicated. Regarding the thermo-mechanical coupling effects in shape memory alloys, in case of high  loading rates, heat generation/absorption during the forward/reverse transformation, will lead in temperature-dependent variation and consequently affects its mechanical behavior. In this paper, a numerical algorithm based on the finite element method is proposed to investigate complex mechanical, thermal, and coupled behavior of shape memory alloys, including both exclusive behaviours of these alloys, that are superelasticity and shape memory effect. Several key examples are simulated and discussed to assess the efficiency and accuracy of proposed algorithm.

The main objective of this paper is to provide an applied algorithm for analyzing propeller-shaft vibrations in marine vessels. Firstly an underwater marine vehicle has been analyzed at different speed in unsteady condition using the finite volume method. Based on the results of this analysis, flow field of marine vehicle (wake of stern) and velocity inlet to the marine propeller  is extracted at different times. Propeller inlet flow field is applied in the boundary element code and using this code, marine propeller has been analyzed in unsteady state. In continue, main / lateral forces and moments over the propeller are extracted. Then the data obtained from the boundary element code alongwith exact geometry of the propeller and shaft have been studied, using finite element code. Natural and forced frequency of the propeller have been determined in various modes of vibration. According to obtained data from Finite Element Method (FEM) numerical analysis, maximum displacement of propeller is for displacement of the propeller tip in forced vibration state

 Grid dispersion is one of the criteria of validating the finite element method (FEM) in simulating acoustic or elastic wave propagation. The difficulty usually arisen when using this method for simulation of wave propagation problems, roots in the discontinuous field which causes the magnitude and the direction of the wave speed vector, to vary from one element to the adjacent one. To solve this problem and improve the response accuracy, two approaches are usually suggested: changing the integration method and changing shape functions. The Finite Element iso-geometric analysis (IGA) is used in this research. In the IGA, the B-spline or non-uniform rational B-spline (NURBS) functions are used which improve the response accuracy, especially in one-dimensional structural dynamics problems. At the boundary of two adjacent elements, the degree of continuity of the shape functions used in IGA can be higher than zero. In this research, for the first time, a two dimensional grid dispersion analysis has been used for wave propagation in plane strain problems using B-spline FEM is presented. Results indicate that, for the same degree of freedom, the grid dispersion of B-spline FEM is about half of the grid dispersion of the classic FEM.

This paper presents a macro model to predict unreinforced masonry structures in plane behavior. The model is based on the concept of multilaminate theory. In the past, the method has been used to model behavior of soil, disregarding the cohesion and the tensile strength. Regarding its mathematical base, and the possibility of applying in other cases, this method is used to predict the ultimate failur load in URM structures in present study. This model is intrinsically capable of spotting induced anisotropy of brittle material such as concrete, rocks and masonry, develponig as a result of cracking. Here, the yield surface applied, consists an generalized mohr-coulomb yield surface, along with a cap model and a cut-off tensile. Comparing numerical results predicted to be obtained in non-linear analysis of masonry structures unreinforced against lateral load, with the results of ther experimental data shows capability of the model in failure analysis of URM structures.

In the present paper thecompressibleflowoftheunderwaterexplosionhasbeensimulatedusing One-fluid
method along with the Eulerian-Lagrangian ALE method. Besides, the exact Riemann solver and an appropriate
equation of state which is consistent with the thermodynamic behavior of water in underwater explosion, is employed.
The two dimensional underwater explosion problem near a flat plate is modeled. In order to increase the accuracy of
the method for simulating the wave front, the adaptive grid is used. The simulated underwater explosion results
agreed well with other similar numerical simulations. The numerical results indicate the capability of the present
study in simulating the physics of underwater explosion and modeling the fluctuations of explosive bubble and also
predicting the creation and collapse of the caviation zone.

: Existence of singular points inside the solution domain or on its boundary deteriorates the accuracy and convergence rate of numerical methods. This phenomenon usually happens due to discontinuities in the boundary conditions or abrupt changes in the domain shape. This study has focused on the solution of singular plate problems using the exponential basis functions method. In this method, unknown functions are considered as a linear combination of exponential basis functions and the coefficients are calculated by approximate satisfaction of the boundary conditions. To increase the accuracy and convergence rate in problems with singular points, a series of singular, quasi-exponential functions are added to the method’s exponential basis functions. These functions have proper discontinuity in location of the singular points and satisfy the homogenous differential equation. The results obtained from the solution of three cracked plate problems show considerable increase in the accuracy and convergence rate of the proposed method compared with the exponential basis functions method without any noticeable increase in the computational cost.

: The gear systems are widely used in industry to transmit the power or change the direction of the torque. Due to the extensive usage of the gears, the detailed designing and the subsequent maintenance of these systems are more and more evident. System recognition can be achieved through modeling the system, investigating the system behavior, and comparing the results obtained through the model with the actual system behavior. Up to now, the effect of dry friction has not been taken into account in nonlinear vibration analysis and modeling of a cracked one-stage gear power transmission system. In this paper, the nonlinear vibration of a pair of cracked spur-gear system in presence of dry friction, static transmission error, clearance and time-variant mesh stiffness is investigated. To this end, the time-variant mesh stiffness of an intact tooth is calculated analytically. Then, the tooth root crack is modeled as a cracked cantilever beam. The governing nonlinear equation of motion is extracted accordingly, and in order to consider the effect of dry friction, the governing equation solved by Rung- Kutta method in three separate time spans. Finally, the frequency response and bifurcation diagrams are used to study the effect of the friction and tooth root crack on the nonlinear vibration behavior of the system.

Having two stable configurations and no need to any permanent energy sources for remaining in each of these stable states, bi-stable composite plates have gained many applications. This paper has concentrated on control and dynamic response of cross ply bi-stable composite plates (0.90). To do this, using Hamilton principle , Rayleigh-Ritz method, and a MATLAB programme specifically designed for this study, have been applied in order to extract  the governing equation of motions in plates. Then, in order to control the large vibration of the cross ply bi-stable plate, a fuzzy controller was proposed using a fuzzy logic and its prformance was simulated by Simulink in Matlab environment. In order to simulate the real conditions on the controller performance, the effect of disturbances and time delay on the responses of controller were also investigated.

Utilizing one of the mesh free methods, the present paper concerns static analysis of thin plates with various geometric shapes based on the mindlin classical plate theories. In this numerical method, the domain of issue is solely expressed through a set of nods and no gridding or element is required. To express the domain of issues with various geometric shapes, first a set of nodes are defined in a standard rectangular domain , then via a three-order map with, these nodes are transferred to the main domain of the original issue; therefore plates of various geometric shapes can be analyzed. Among meshfree numerical methods, Element Free Galerkin method (EFG) is utilized here. The method is one of the weak form integral methods that uses MLS shape functions for approximation. Regarding the absence of Delta feature in MLS functions, boundary conditions cannot be imposed directly; hence the Lagrangian method is utilized to impose boundary conditions. At the end, our outputs are compared with those of analytic and finite element methods for plates, in order to validate the exactness of our solution method, and then after reliability is established, a few new examples will be solved.

The present paper studies the effect of creating a fillet on fretting fatigue strength of an axle, using different multiaxial fatigue criteria and fretting fatigue damage parameter. Finite element method is applied to obtain stress and strain in the axle and the results obtained from modeling are compared with the experimental test data available in literature. The results show that fretting fatigue strength of the axle and fracture area depends on the ratio of  diameter to fillet radius. Multiaxial fatigue criteria is almost capable of estimating the fatigue strength of the axle . However; the results obtained from investigating fretting fatigue damage parameter are almost in accordance with the results of experimental data and consequently fretting fatigue damage parameter can be appropriately used as a criterion for estimating fretting fatigue strength of the axles.

Weighted Simulation-based Design Method (WSDM) is recently developed as an efficient method for Reliability-
Based Design Optimization (RBDO). Despite simplicity, this method degrades effectiveness to obtain accurate optimum design for
high dimension RBDO. Besides, its application range is restricted to RBDOs including only random design variables. In the
present study, local search strategy is employed to enhance the accuracy of conventional WSDOM, and to reduce the computational cost. Besides, a shifting strategy is proposed to increase the application range of WSDM for handling general RBDO problems. The efficiency of the proposed methods is investigated by solving some structural reliability problems.
Comparisonof the obtained results with exact solutions confirms accuracy and superiority of the proposed method for
solving various engineering problems.

In this article, the vibration analysis of a set of parallel Timoshenko beams connected by intermediate flexible connections, with arbitrary numbers, is studied. The moving load is a vehicle, which is modeled by a two-axle six degrees of freedom system, as a mass-spring-damper system, in a plane motion. For the solution, a new method is proposed which uses a change of variables strategy to decouple the system of differential equations. For this purpose, the stiffness matrix obtained from each column of intermediate connections should have the same normalized eigenvectors. The displacements and the bending moments of the beams and the vehicle due to changes in the stiffness of connections and changes in speeds will be examined. Finally, the validity of the results are measured.