Development of an object-oriented finite element program: application to metal-forming and impact simulations

During the last 50 years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. In the same time, the finite element method has become a widely used tool for researchers and engineers. Recent advances in computational software have made possible to solve more physical and complex problems such as coupled problems, nonlinearities, high strain and high-strain rate problems. In this field, an accurate analysis of large deformation inelastic problems occurring in metal-forming or impact simulations is extremely important as a consequence of high amount of plastic flow. In this presentation, the object-oriented implementation, using the C++ language, of an explicit finite element code called DynELA is presented. The object-oriented programming (OOP) leads to better-structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. The most significant advantage of OOP is in the modeling of complex physical systems such as deformation processing where the overall complex problem is partitioned in individual sub-problems based on physical, mathematical or geometric reasoning. We first focus on the advantages of OOP for the development of scientific programs. Specific aspects of OOP, such as the inheritance mechanism, the operators overload procedure or the use of template classes are detailed. Then we present the approach used for the development of our finite element code through the presentation of the kinematics, conservative and constitutive laws and their respective implementation in C++. Finally, the efficiency and accuracy of our finite element program are investigated using a number of benchmark tests relative to metal forming and impact simulations

A Multidisciplinary Tool for Systems Analysis of Planetary Entry, Descent, and Landing (SAPE)

SAPE is a Python-based multidisciplinary analysis tool for systems analysis of planetary entry, descent, and landing (EDL) for Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Titan. The purpose of SAPE is to provide a variable-fidelity capability for conceptual and preliminary analysis within the same framework. SAPE includes the following analysis modules: geometry, trajectory, aerodynamics, aerothermal, thermal protection system, and structural sizing. SAPE uses the Python language-a platform-independent open-source software for integration and for the user interface. The development has relied heavily on the object-oriented programming capabilities that are available in Python. Modules are provided to interface with commercial and government off-the-shelf software components (e.g., thermal protection systems and finite-element analysis). SAPE runs on Microsoft Windows and Apple Mac OS X and has been partially tested on Linux

Three-Dimensional Finite Element Analysis of Composite Laminates Subjected to Transverse Impact

An interest in the low velocity impact probkins has been revived with the advent of laminated composite materials and their increasing use in aerospace and other applications. The reason for this new activity is that despite certain advantages of these materials over more traditional materials, composites are known to be vulnerable to impact. Impacts may occur anywhere during manufacture, normal operations,or maintenance and may induce significant internal damage in the form of matrix cracking, delarnination or fibre breakage, that are undetectable by visual inspection and cause significant reductions in the strength and stability of the structure. In the present paper. a three-dimensional finite element and transient dynamic analysis of fibre-reinforced polymer matrix composite laminates (e.g. graphite/epoxy, glass/epoxy, etc.) subjected to transverse foreign object impact is performed. Layered version of eight-noded isoparametric brick element with incompatible modes is used to model the laminate. Transient dynamic equilibrium equation is integrated step-by-step with respect to time using Newmark direct time integration method. Non-linear contact law reported in literature is used to model the local contact behavior and the timevartiing contact force is calculated based on the relative displacement between impactor and laminate using Newton-Raphson method. Based on the finite element model, a versatile computer software was developed in C++ programming language using object- oriented approach. The software can be used to determine several results such as contact force history, displacement and velocity histories of impactor and the timevarying displacements, forces, strains and stresses throughout the laminate. Some example problems are considered to study the effects of impactor velocity and laminate boundary conditions on impact behavior of graphite/epoxy composite laminates, and results are presented for time-history of contact force and laminate central deflection.The transient dynamic strains and stresses inside the laminate were also calculated for few case

Numerical simulation of the stress-strain state of the dental system

We present mathematical models, computational algorithms and software, which can be used for prediction of results of prosthetic treatment. More interest issue is biomechanics of the periodontal complex because any prosthesis is accompanied by a risk of overloading the supporting elements. Such risk can be avoided by the proper load distribution and prediction of stresses that occur during the use of dentures. We developed the mathematical model of the periodontal complex and its software implementation. This model is based on linear elasticity theory and allows to calculate the stress and strain fields in periodontal ligament and jawbone. The input parameters for the developed model can be divided into two groups. The first group of parameters describes the mechanical properties of periodontal ligament, teeth and jawbone (for example, elasticity of periodontal ligament etc.). The second group characterized the geometric properties of objects: the size of the teeth, their spatial coordinates, the size of periodontal ligament etc. The mechanical properties are the same for almost all, but the input of geometrical data is complicated because of their individual characteristics. In this connection, we develop algorithms and software for processing of images obtained by computed tomography (CT) scanner and for constructing individual digital model of the tooth-periodontal ligament-jawbone system of the patient. Integration of models and algorithms described allows to carry out biomechanical analysis on three-dimensional digital model and to select prosthesis design.Comment: 19 pages, 9 figure

Object oriented design of a thermo-mechanical FEM code

An object oriented design is presented for a computer program that can perform\ud thermo-mechanically coupled analyzes. The target of the design is a \ud exible and robust\ud computer program. It should be easy to adapt and extend, re-using existing code, without\ud interfering with already established algorithms.\ud The program uses publicly available toolkits that are currently emerging as C++ pack-\ud ages. First of all the Standard C++ Library (formerly Standard Template Library) is\ud used for packing items in container classes. Secondly the matrix and vector operations\ud are derived from the Template Numerical Toolkit (TNT) and �nally (not essentially for\ud the numerical part) a graphical user interface is made, based on the wxWindows package,\ud that can generate a GUI for Motif and MS-Windows with the same code.\ud Attention is given to the design of classes such as speci�c elements and material classes\ud based on more general classes. A hierarchy of classes is constructed where general behavior\ud is put high in the hierarchy and speci�c behavior low. The choice between inheritance and\ud aggregation is made at several levels

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part II: application to partial differential equations

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application

Specifying Reusable Components

Reusable software components need expressive specifications. This paper outlines a rigorous foundation to model-based contracts, a method to equip classes with strong contracts that support accurate design, implementation, and formal verification of reusable components. Model-based contracts conservatively extend the classic Design by Contract with a notion of model, which underpins the precise definitions of such concepts as abstract equivalence and specification completeness. Experiments applying model-based contracts to libraries of data structures suggest that the method enables accurate specification of practical software

Automated Verification of Design Patterns with LePUS3

Specification and [visual] modelling languages are expected to combine strong abstraction mechanisms with rigour, scalability, and parsimony. LePUS3 is a visual, object-oriented design description language axiomatized in a decidable subset of the first-order predicate logic. We demonstrate how LePUS3 is used to formally specify a structural design pattern and prove (‗verify‘) whether any JavaTM 1.4 program satisfies that specification. We also show how LePUS3 specifications (charts) are composed and how they are verified fully automatically in the Two-Tier Programming Toolkit

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part I: template-based generic programming

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering