In sheet forming processes, using Forming Limit Diagrams (FLDs) in study of formability and designi die is very important. One method to achieve the curves of FLDs that has validate and appropriate results is Marciniak-Kuczynski model. This model is a way to predict the local necking. In the present study, FLDs were achieved by imposing the theoretical Marciniak–Kuczynski model in two different Finite element model and using Abaqus. In the first model, the theory of Marciniak–Kuczynski was imposed to Finite element of Nakazima test and in second one (Flat), the theory of Marciniak–Kuczynski was simulated. The input data for these simulations was obtained from tension tests in three different directions. After comparing the results of Flat and Nakazima Finite element model with empirical results, the FLD obtained from the Finite element of Nakazima test was valid and less than 10 percent below the empirical FLD. Bending is the reason of difference between FLD obtained from Flat model and empirical one.

Determining the ordering quantity is one of the most important and at the same time , the most difficult issue of production planning which has extensively received particular attention in production planning.This paper aims is presenting an initiative method of determining the ordering quantity with production capacity restaiction for a non-shortage state. The method starts with a preliminary answer for the whole areas of planning and attempts to justify the appropriateness of the answers and reduce the costs as much as possible. the most remarkable features of this proposed model is reduced amount of calculation along with a satisfactory attained results which is shown by an example.

one of the simplest numerical integration method which provides a large saving in computational efforts, is the well known one-point Gauss quadrature which is widely used for 4 nodes quadrilateral elements. On the other hand, the biggest disadvantage to one-point integration is the need to control the zero energy modes, called hourglassing modes, which arise. The efficiency of four different anti-hourglassing approaches, Flanagan (elastic approach), Dyna3d, Hansbo and Liu have been investigated. The first two approaches have been used in 2 and 3-D explicit codes and the latter have been employed in 2-D implicit codes. For 2-D explicit codes, the computational time was reduced by 55% and 60% for elastic and Dyna3d, respectively. However, for 3-D codes the reduction was dependent on the number of elements and was obtained between 50% and 70%. Also, the error due to the application of elastic methods was less than that for Dyna3d when the results were compared with those obtained from 2-points Gauss quadrature. Nevertheless, the convergence occurred more rapidly and the oscillations were damped out more quickly for Dyna3d approach. For implicit codes, the anti-hourglassing methods had no effect on the computations and therefore a 2-points Gauss quadrature is recommended for implicit codes as it provide the results more accurately

For rubble mound breakwaters, incorporating a berm in the seaward slope can be very effective in reducing wave overtopping and mitigating wave loads acting on the breakwater armor elements. This research aims to investigate the effect of horizontal berm on the seismic response of conventional rubble mound breakwaters, considering various amplitudes and frequencies characterizing seismic loads. Finite element models of conventional rubble mound breakwaters, with and without berm, are developed using Plaxis 2D software for this purpose. Additionally, the stability of rubble mound breakwaters with berms is studied through various numerical models, considering different lengths and height levels of the berm. A comparative analysis of the results shows that rubble mound breakwaters incorporating berms exhibit lower deformation characteristics compared to those without berm. The numerical study results suggest that berms can significantly enhance the stability and reduce displacements of rubble mound breakwaters under seismic loading compared to breakwaters without berm.

Wavelet Analysis has called the attentions in numerical solutions of PDEs in recent years. Because of orthogonality and compact support of Daubechies scaling functions, these functions have excellent ability of providing good accuracy and convergence for the approximation of the solution in singularities. In this article the method of using these functions for numerical solving of PDE for Euler–Bernoulli beams is formulated. This procedure needs to calculate derivatives and integrals of scaling functions as the shape functions of wavelet-based Finite element method. Because of non-explicit formulation and high oscillation of these functions, conventional methods -like Gauss method for integration- are not suitable and accurate. Thus some special methods are formulated for these requirements. The ability and high accuracy of wavelet-based beam element for different boundary conditions and loads is shown in some examples.

The main part of Finite element analysis via the force method involves the formation of a suitable null basis for the equilibrium matrix. For an optimal analysis, the chosen null basis matrices should exhibit sparsity and banding, aligning with the characteristics of sparse, banded, and well-conditioned flexibility matrices. In this paper, an effective method is developed for the formation of null bases of Finite element models (FEMs) consisting of shell elements. This leads to highly sparse and banded flexibility matrices. This is achieved by associating specific graphs to the FEM and choosing suitable subgraphs to generate the self-equilibrating systems (SESs) on these subgraphs. The effectiveness of the present method is showcased through two examples.

This paper presents element-free Galerkin (EFG) method as a computational technique that can effectively avoid the disadvantage of mesh entanglement. The present method is used to analyze the static defelection of beams. The moving least squares (MLS) approximation has been used for constructing the shape function based on a set of nodes arbitrarily distributed in the analysis domain.

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.

In this paper an efficient method is developed for the formation of null bases of Finite element models comprised of four-node quadrilateral plane stress and plane strain elements corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs to the Finite element models and using an element with new equilibrium tractions and stress field for the formation of localized self-equilibrating stress systems. The efficiency of the present method is illustrated through some examples.