Journal of Numerical Methods in Civil Engineering
Volume:3 Issue: 1, Sep 2018

In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versions of the Finite Element Method known in solid mechanics, the adaptive Galerkin Finite Element Method (GFEM) and Extended Finite Element Method (XFEM), for the two dimensional fracture analysis of structures. After the discretization of the governing equations, the above three methods are implemented in FORTRAN. In the adaptive GFVM and GFEM methods, the discrete crack concept is used to model the crack surface, but in the XFEM, the crack surface is modeled through the enrichment of the displacement approximation around the crack. Several test cases are used to validate the developed dimensional numerical models for the analysis of cracked structures. After verification, the fracture analysis of a plate under pure mode I and mixed mode I/II is performed using the above-mentioned numerical methods. The numerical results show that three methods accurately calculate the stress intensity factors. The average percent error of the XFEM, adaptive GFEM and adaptive GFVM is ,  and , respectively. The results show that the CPU time of the adaptive GFVM is 5.5 and 3 times less than the XFEM and adaptive GFEM, respectively.

The lateral-torsional buckling of tapered thin-walled beams with singly-symmetric cross-section has been investigated before. For instance, the power series method has been previously utilized to simulate the problem, as well as the finite element method. Although such methods are capable of predicting the critical buckling loads with the desired precision, they need a considerable amount of time to be accomplished. In this paper, the finite difference method is applied to investigate the lateral buckling stability of tapered thin-walled beams with arbitrary boundary conditions. Finite difference method, especially in its explicit formulation, is an extremely fast numerical method. Besides, it could be effectively tuned to achieve a desirable amount of accuracy. In the present study, all the derivatives of the dependent variables in the governing equilibrium equation are replaced with the corresponding forward, central and backward second order finite differences. Next, the discreet form of the governing equation is derived in a matrix formulation. The critical lateral-torsional buckling loads are then determined by solving the eigenvalue problem of the obtained matrix. In order to verify the accuracy of the method, several examples of tapered thin-walled beams are presented. The results are compared with their counterparts of finite element simulations using shell element of known commercial software. Additionally, the result of the power series method, which has been previously implemented by the authors, are considered to provide a comparison of both power series and finite element methods. The outcomes show that in some cases, the finite difference method not only finds the lateral buckling load more accurately, but outperforms the power series expansions and requires far less central processing unit time. Nevertheless, in some other cases, the power series approximation has less relative error. As a result, it is recommended that a hybrid method, based on a combination of the finite difference technique and the power series method, be employed for lateral buckling analysis. This hybrid method simultaneously inherits its performance and accuracy from both mentioned numerical methods.

In this paper, by using a finite element model, the in-plane drift effect on the out-of-plane behavior of the infilled frame with weak infill walls has been calculated. Therefore, the out-of-plane and in-plane interaction for infill walls of different slenderness/aspect ratios, bond tension strengths and separated gap types, has been evaluated. The results are shown that infill walls having full contact at the top of the wall but isolated from columns have larger out-of-plane capacities than those isolated from beam and columns. However, infill walls having full contact at the top are more vulnerable to in-plane drifts. Also, the effect of the in-plane drift on the out-of-plane capacity of the separated infill wall can be noticeable. The results are indicated the out-of-plane capacity of the separated infill wall has been found to be inversely proportional to slenderness ratio and aspect ratio values and directly proportional to bond tension strength.

In the present study, shear displacements were calculated for all failure surface slices in earth slopes using the limit equilibrium method. To this end, the hyperbolic shear stress-strain constitutive law was applied. Local factors of safety were determined for the slices based on stress and displacement values. In order to calculate the displacement of earth slopes using the proposed method, a numerical model was developed satisfying the equilibrium of forces by a trial and error approach. A comparison between shear displacements obtained from this study in examples 1 and 2, with those obtained from FEM analysis which has yielded the normal errors of about 1.066% and 0.52%, respectively. Eventually, the effects of failure ratio ( ), and hyperbolic stiffness parameters (n and k) on displacement of earth slopes were examined.

Although concrete slabs have an extensive use in structures due to their architectural and executive benefits, the suitability of their behavior against the progressive collapse phenomenon has always been questioned. This study numerically investigates the step-by-step behavior of a support-removed flat slab floor with square panels under the effect of partial overloading. After validation of the modeling method, parts of the designed floor are exposed to increasing downward and uniformly distributed loading during three separate analyses that correspond to the removal of supporting corner, penultimate and interior columns. The pattern of stress in the slab reinforcement and propagation of cracks in the concrete are presented. The findings showed high concentration of slab damage around the corner columns located in the perimeter of overloaded panels and highlighted the role of slab add bars embedded in the vicinity of exterior columns against failure. It was also shown that, unlike the frame-type structural systems, stress redistribution occurs considerably along the diagonals of the slab panels directly connected to the failed support.

The selection of a suitable numerical method to evaluate the dynamic behavior of structures, especially in nonlinear cases, is an important task in practice. Accordingly, the purpose of this study is to demonstrate the numerical features of a new single-step type of the Modified Energy Method (MEM) to compute the dynamic response of structural systems. A comprehensive formulation of this energy-based time integration scheme to incorporate the general nonlinear behavior in MDOF systems is presented for the first time ever in this paper. After discussing the stability and accuracy of the proposed time-stepping integration procedure, five applicable numerical examples in structural dynamics and earthquake engineering practices involving the various hysteretic behaviors and the effects of consistent mass and non-classical damping matrices are examined by the presented technique. In each case, the relevant comparisons are given in accordance to other available methods (e.g., Newmark and Runge-Kutta). Overall, the results indicate that the MEM yields a better accuracy than the 2nd Runge-Kutta approach. Furthermore, the distinguishing feature of the proposed method is to provide information about choosing the optimal size of the time intervals, especially in the nonlinear analyzes, which is not achievable in other applicable approaches.