استراتژی برنامه ریزی شی گرا AC برای اجرای تجزیه و تحلیل حساسیت المان محدود برای یک مدل مواد ساختاری غیر خطی

The Finite Element Method (FEM) has become the most popular numerical method for solving a wide variety of complex engineering problems. However, from the programming point of view, when a FEM program has a lot of computational capabilities it is very difficult to maintain and enlarge the program codes. Recently the object-oriented programming paradigm has become a powerful method for overcoming such difficulties. This paper contains the description of an open environment for the FEM, written in C++, with explanations about how the sensitivity analysis and the non-linear material behaviour (damage models) have been taken into account.

The continuous increase of the capabilities of hardware and software tools allows to solve very complex structural problems. Nowadays, the use of new materials, new industrial processes and coupling between different physical phenomena can be considered altogether. This has produced a progressive substitution of the traditional experimental methods by the less expensive numerical analysis. Since the very beginning, the task of programming the Finite Element Method FEM has been increasing in difficulty over the years. The more that engineers want to compute the more difficult it becomes to implement. The reasons rise in the difficulty of the mathematical boundary problems and in the language and programming strategies. In this paper the authors present an overview of the FEM programming drawbacks and comment their experience with different programming strategies. Finally, an object-oriented approach for the implementation of non-linear material behaviour and its sensitivity analysis is described.

The programming techniques used for the implementation of the FEM have always been strongly linked with the available programming languages. Nowadays, the object-oriented programming is an interesting alternative for the production of finite element codes easy to maintain and to expand. In this work, the transition from a linear elastic code to a non-linear material model with arc-length and sensitivity analysis has been presented. The success of this implementation relays in the object-oriented programming. Generally speaking, most of the authors agree in the correct adaptation of the finite element strategies to the object-oriented coding. Nevertheless, we want to emphasise that due to the implicit philosophy of the FEM, the maximum performance of the object-oriented systems is only achieved if they are combined with some procedural coding parts. In this context, C++ is, nowadays, the best developing language for the FEM. We have experienced that during the development of object-oriented codes the time dedicated by the programmer to the organisation of the information and its management is much bigger than in the procedural programming case. This is because the object orientation requires a higher level of rigour. There must be taking account that an inconvenient of the object-oriented programming appears when the class organisation is incorrect and an abuse in the number of objects and in the privacy of data is produced. In this sense, the object-oriented programming is not a flexible tool. Nevertheless, the generation of new classes and the expansion of computation capabilities are generally facilitated, particularly thanks to the inheritance. The results obtained in the solution of the presented example show the good performance not only of the proposed formulation, but also of its implementation using the object-oriented approach. Finally, we conclude that the expansion possibilities of the object-oriented codes are much bigger than in the code produced using procedural languages.