Mohammad Malekan

AN OBJECT-ORIENTED CLASS ORGANIZATION FOR GLOBAL-LOCAL GENERALIZED FINITE ELEMENT METHOD

THIS PAPER SHOWS AND DISCUSSES A GENERIC IMPLEMENTATION OF THE GLOBAL-LOCAL ANALYSIS TOWARD GENERALIZED FINITE ELEMENT METHOD (GFEMGL). THIS IMPLEMENTATION, PERFORMED INTO AN ACADEMIC COMPU-TATIONAL PLATFORM, FOLLOWS THE OBJECT-ORIENTED APPROACH PRESENTED BY THE AUTHORS IN A PREVIOUS WORK FOR THE STANDARD VERSION OF GFEM IN WHICH THE SHAPE FUNCTIONS OF FINITE ELEMENTS ARE HIERARCHICALLY ENRICHED BY ANALYTICAL FUNCTIONS, ACCORDING TO THE PROBLEM BEHAVIOR. IN GLOBAL-LOCAL GFEM, HOWEVER, THE ENRICHMENT FUNCTIONS ARE CONSTRUCTED NUMERICALLY FROM THE SOLUTION OF A LOCAL PROBLEM. THIS STRATEGY ALLOWS THE USE OF A COARSE MESH EVEN WHEN THE PROBLEM PRODUCES COMPLEX STRESS DISTRIBUTIONS. ON THE OTHER HAND, A LOCAL PROBLEM IS DEFINED WHERE THE STRESS FIELD PRESENTS HIGH GRADIENTS AND IT IS DISCRETIZED USING A LARGE NUMBER OF ELEMENTS. THE RESULTS OF THE LOCAL PROBLEM ARE USED TO ENRICH THE GLOBAL PROBLEM WHICH IMPROVES THE APPROXIMATE SOLUTION. THE GREAT ADVANTAGE IS ALLOWING A WELL-REFINED DESCRIPTION OF THE LOCAL PROBLEM, WHEN NECESSARY, AVOIDING AN OVERBURDEN FOR THE COMPUTATION OF THE GLOBAL SOLUTION. DETAILS OF THE IMPLEMENTATION ARE PRESENTED AND IMPORTANT ASPECTS OF USING THIS STRATEGY ARE HIGHLIGHTED IN THE NUMERICAL EXAMPLES.

A computational framework for a two-scale generalized/extended finite element method: Generic imposition of boundary conditions

Purpose This paper aims to present a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon/phenomena. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having global- and local-scale components. This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately by using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution. Design/methodology/approach The implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analyses models with the partition of unity enrichment scheme. Beside the extension of the G/XFEM implementation to enclose the global–local strategy, the imposition of different boundary conditions is also generalized. Findings The generalization done for boundary conditions is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are used, and the accuracy, robustness and computational efficiency are demonstrated. Originality/value This work shows a generalize imposition of different boundary conditions for global–local G/XFEM analysis through an object-oriented implementation. This generalization is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problems simultaneously and solving plate problems using global–local G/XFEM are other contributions of this work.

IMPOSITION OF DIRICHLET BOUNDARY CONDITIONS IN ELEMENT FREE GALERKIN METHOD THROUGH AN OBJECT-ORIENTED IMPLEMENTATION

ONE OF THE MAIN DRAWBACKS OF ELEMENT FREE GALERKIN (EFG) METHOD IS ITS DEPENDENCE ON MOVING LEAST SQUARE SHAPE FUNCTIONS WHICH DON’T SATISFY THE KRONECKER DELTA PROPERTY, SO IN THIS METHOD IT’S NOT POSSIBLE TO APPLY DIRICHLET BOUNDARY CONDITIONS DIRECTLY. THE AIM OF THE PRESENT PAPER IS TO DISCUSS DIFFERENT ASPECTS OF THREE WIDELY USED METHODS OF APPLYING DIRICHLET BOUNDARY CONDITIONS IN EFG METHOD, CALLED LAGRANGE MULTIPLIERS, PENALTY METHOD, AND COUPLING WITH FINITE ELEMENT METHOD. NUMERICAL SIMULATIONS ARE PRESENTED TO COMPARE THE RESULTS OF THESE METHODS FORM THE PERSPECTIVE OF ACCURACY, CONVERGENCE AND COMPUTATIONAL EXPENSE. THESE METHODS HAVE BEEN IMPLEMENTED IN AN OBJECT-ORIENTED PROGRAMING ENVIRON-MENT, CALLED INSANE, AND THE RESULTS ARE PRESENTED AND COMPARED WITH THE ANALYTICAL SOLUTIONS.

Two-dimensional fracture modeling with the generalized/extended finite element method: An object-oriented programming approach

Abstract This work presents an object-oriented implementation of the G/XFEM to model the crack nucleation and propagation in structures made of either linear or nonlinear materials. A discontinuous function along with the asymptotic crack-tip displacement fields are used to represent the crack without explicitly meshing its surfaces. Different approach are explained in detail that are used to capture the crack nucleation within the model and also determine the crack propagation path for various problems. Stress intensity factor and singularity of the localization tensor (which provides the classical strain localization condition) can be used to determine the crack propagation direction for linear elastic materials and nonlinear material models, respectively. For nonlinear material model, the cohesive forces acting on the crack plane are simulated in the enrichment process by incorporating a discrete constitutive model. Several algorithms and strategies have been implemented, within an object-oriented framework in Java, called INSANE. This implementation will be presented in detail by solving different two-dimensional problems, for both linear and nonlinear material models, in order to show the robustness and accuracy of the proposed method. The numerical results are compared with the reference solutions from the analytical, numerical or experimental results, where applicable.

Semiautonomous Mission Operation Plan for a Remote Sensing Leo Microsatellite

AbstractMission operation planning is a critical and multidisciplinary feature in conducting satellite missions. Satellite operations can be divided into three phases: initial phase, operational or nominal phase, and disposal. All the tasks of these phases might be handled onboard, using a specified level of autonomy. On the other hand, a combination of onboard management and ground station (GS) telecommands can be used to perform the mentioned tasks. In the present work, a mission operation plan has been developed for a remote sensing low earth orbit (LEO) microsatellite using the semiautomated method, covering all operational phases of the satellite. The proper level of in-orbit autonomy enables the satellite to perform mission-specified tasks when out of ground station coverage. Additionally, microsatellite operational architecture for all in-orbit phases is presented. A basic timetable of the onboard control procedure is described, representing the satellite mission tasks and their corresponding seque...