Tetrahedral finite element mesh generation from NURBS solid models

In this paper, the development and the implementation of a tetrahedral meshing algorithm for generation of finite element meshes from NURBS solid models is presented. The meshing algorithm is based on a Delaunay technique, and makes use of some spatial data structures. The algorithm is capable of generating both uniform and varying size four-node and ten-node tetrahedral meshes. The algorithm has been implemented in a building block approach as part of a software library. It has been used as a practical tool in engineering design processes. Several representative test cases illustrate the effectiveness of the automatic solid mesh generator.     

Three-dimensional mesh generation using principles of finite element method

The present work deals with the development of a three-dimensional mesh generation algorithm using the principles of FEM with special emphasis on the computational efficiency and the memory requirement. The algorithm makes use of a basic mesh that defines the total number of elements and nodes. Wavefront technique is used to renumber the nodes in order to reduce the bandwidth. By elastic distortion of the basic mesh, it is redefined to map onto actual geometry to be discretized. Later a finer distribution of mesh is done in the zones of interest to suit the nature of the problem. The same Finite Element code meant for stress analysis is adopted with necessary modifications. The algorithm has been extended to three-dimensional geometries. The current methodology is used to discretize a straight bevel gear and an hourglass worm to study their stress patterns.     

A hybrid expert system for finite element modeling of fuselage frames

A hybrid expert system which integrates expert system with neural networks is developed for finite element modeling of fuselage frame of aircraft structure. Importance order parameters are introduced to quantify the modeling control. Expert knowledge of importance order parameters, node setting and element selection in fuselage frame modeling is presented. A neural network is employed to structure type classification. The modeling procedures of fuselage frame can be carried out automatically and efficiently by this system. Example shows the frame 1022 of MD-82 passenger aircraft which is modeled by this system automatically and successfully.     

Fuzzy logic-based expert system to predict the results of finite element analysis

In this paper, a fuzzy logic (FL)-based expert system (ES) has been developed to predict the results of finite element (FE) analysis, while solving a rubber cylinder compression problem. As the performance of an ES depends on its knowledge base (KB), an attempt is made to develop the KB through three different approaches by using a genetic algorithm (GA). To collect the training data, two input parameters, namely element size and shape ratio are varied, while solving the said physical problem using an FEM package. The performance of the trained fuzzy logic-based expert system is tested for several test cases, differing significantly from the training cases. Results of these approaches are compared with those of FE analysis. Once developed, the ES is able to determine the values of parameters to be used in FE analysis, in order to obtain the results within a reasonable accuracy, at the cost of a much lower computation compared to that of the FEM package itself.     

Intelligent finite element mesh generation

A knowledge-based and automatic finite element mesh generator (INTELMESH) for two-dimensional linear elasticity problems is presented. Unlike other approaches, the proposed technique incorporates the information about the object geometry as well as the boundary and loading conditions to generate an a priori finite element mesh which is more refined around the critical regions of the problem domain. INTELMESH uses a blackboard architecture expert system and the new concept of substracting to locate the critical regions in the domain and to assign priority and mesh size to them. This involves the decomposition of the original structure into substructures (or primitives) for which an initial and approximate analysis can be performed by using analytical solutions and heuristics. It then uses the concept of wave propagation to generate graded nodes in the whole domain with proper density distribution. INTELMESH is fully automatic and allows the user to define the problem domain with minimum amount of input such as object geometry and boundary and loading conditions. Once nodes have been generated for the entire domain, they are automatically connected to form well-shaped triangular elements ensuring the Delaunay property. Several examples are presented and discussed. When incorporated into and compared with the traditional approach to the adaptive finite element analysis, it is expected that the proposed approach, which starts the process with near optimal initial meshes, will be more accurate and efficient.     

An expert system for setting time steps in dynamic finite element programs

An expert system, ETUDES—Expert Time integration control Using Deep and Surface Knowledge System, which addresses the determination of the timestep for time integration of linear structural dynamic equations is described. This time-step may also be applicable for a moderately nonlinear simulation of the same structure. The program also determines whether an explicit or implicit method is most efficient for the particular simulation. A production rule programming system written in OPS5 is used for the implementation of this prototype expert system. Issues relating to the expert system architecture for this application, such as knowledge representation and structure, as well as domain knowledge are discussed. The prototype is evaluated by measuring it's performance in various benchmark model problems.     

Automatic generation of finite element meshes

This paper describes a new algorithm for the automatic generation of finite element meshes of arbitrary multiply connected domains. The strategy is based upon the construction of a mapping from the generated mesh into a regular one. The scheme is designed for maximum flexibility and is able to generate meshes of triangular or quadrilateral curved elements. Several examples are presented to illustrate the applicability of the algorithm.     

Nonlinear finite element analysis of concrete structures using new constitutive models

Nonlinear finite element analysis was applied to various types of reinforced concrete structures using a new set of constitutive models established in the fixed-angle softened-truss model (FA-STM). A computer code FEAPRC was developed specifically for application to reinforced concrete structures by modifying the general-purpose program FEAP. FEAPRC can take care of the four important characteristics of cracked reinforced concrete: (1) the softening effect of concrete in compression, (2) the tension-stiffening effect by concrete in tension, (3) the average (or smeared) stress–strain curve of steel bars embedded in concrete, and (4) the new, rational shear modulus of concrete. The predictions made by FEAPRC are in good agreement with the experimental results of beams, panels, and framed shear walls.     

An equilibrium method for stress calculation using finite element displacement models

The stress computation concept described in [1]is extended here to arbitrary meshes and elements — in particular to triangular elements. After calculating the nodal displacements — using complete and conforming displacement models — we assume linear stress distributions and corresponding virtual displacements at element peripheries. The nodal stress values are then determined by the principle of virtual work. The right-hand side of the resulting system of algebraic equations consists of the work done by the known nodal stress resultants acting along the virtual displacements. In general, the system of equations is nonquadratic on the structural level. Gauss's transformation produces a symmetric, positive definite band matrix. This kind of stress calculation is called the equilibrium method.A dual node method is also given. It involves the inversion of element matrices instead of the master matrix.Various examples of plane stress, plate bending and shell problems show much better accuracy of stresses in comparison with conventional methods. Furthermore, these techniques improve the computational efficiency considerably. There is also a special advantage in the possibility of choosing arbitrary subregions of the structure for stress calculation.     

The application of an expert system shell to an unstructured domain of expertise: using expert system technology to teach SSM

Action research is orchestrated by the interaction between theory and practice as exemplified by soft systems methodology (SSM). The use of computers has traditionally been developed out of what has been referred to as the ‘rationalistic’ tradition which represents the search for solutions for pre-determined, logical goals (Winograd & Flores, 1986). Action research anticipates the need to explore and learn about each intervention into human activity, using models thought to be relevant to thinking about the world to help structure the learning process. In comparison, the ‘rationalistic’ tradition seeks universal laws for behaviour and uses validated models of the reality represented by these laws to solve problems. It would seem, therefore, that to translate SSM into a computer-based format would be dialectically opposed to the intellectual framework in which the methodology is seated. However, the authors suggest that there is one area in which a computer-based version of SSM may be useful. This paper describes an exploratory study of the application of expert system technology as an aid to teaching SSM.     

Attribute specification for finite element models

Two different approaches for the application of problem specific attributes to finite element models are discussed. In both approaches interactive computer graphics techniques and the use of a top-down program approach is emphasized. The major difference in the approaches is the point during problem definition that the attributes are applied and manifests itself primarily in the program's database with little effect on program operation. Program operation is demonstrated through the use of an example problem. Finally, the advantages and disadvantages of the two approaches are discussed.     

Generative design in architecture using an expert system

The mathematician-architect Christopher Alexander has devised a theory of objective architectural design. He believes that all architectural forms can be described as interacting patterns, all possible relationships of which are governed by generative rules. These form a ‘pattern language’ capable of generating forms appropriate for a given environmental context. The complexity of interaction among these rules leads to difficulties in their representation by conventional methods. This paper presents a Prolog-based expert system which implements Alexander's design methodology to produce perspective views of partially and fully differentiated 3-dimensional architectural forms.     

Automatic mesh generation for finite element analysis

The finite element analysis in engineering applications comprises three phases: domain discretization, equation solving and error analysis. The domain discretization or mesh generation is the pre-processing phase which plays an important role in the achievement of accurate solutions. In this paper, the improvement of one particularly promising technique for generating two-dimensional meshes is presented. Our technique shows advantages and efficiency over some currently available mesh generators.     

Graphical representation of models and results in the finite element system COSAR

The finite element method has become one of the most-used calculation procedures in various fields of engineering in recent years. Due to progress in hardware architecture and computer graphics, the efficiency of its application could increase decisively. Notably, the solution of complex problems would be unthinkable today without the availability of powerful graphic processors.

In connection with the development of the finite element system COSAR at the Technical University Magdeburg, various graphic processors were created. In this paper, these processors are introduced. Information is given about interactive techniques for the generation of finite element models, about checking procedures for complex 3D structures by graphical means, and about possibilities for result presentation with colored pictures. Requirements for hardware architecture and software tools in the field of graphical input and output are discussed.     

Finite element mesh design expert system

The paper presents a consultative rule-based expert system for finite element mesh design. The aim of the expert system presented is to propose the appropriate type of the finite elements and determine the resolution values for the finite element mesh to be used for the analysis. The extensive knowledge base, comprising about 1900 rules, was built mainly by the use of machine learning (ML) techniques. Several examples will confirm that an expert system shell written in Prolog enables efficient use of the knowledge base and adequate communication between the system and the user. The system has the ability to explain the inference process. Thus, it can also be used as a teaching tool for inexperienced users—students. The results of the experimental use of the system are encouraging and can be used as guidelines for further developments and improvements of the system.     

Realization of distributed system models using code generation extensions

Development of distributed software systems is complex due to the distribution of resources, which complicates validation of system-wide functionality. Such systems include various facets like functionality and distribution, each of which must be validated and integrated in the final software solution. Model-based techniques advocate various abstraction approaches to cope with such challenges. To enhance model-based development, this paper proposes (1) guidelines for development of distributed systems, where the different facets are introduced gradually through systematic modeling extensions, (2) code generation capabilities supporting technology specific realizations, and (3) demonstration of the applicability of our approach using an industrial case study involving the development of a harvest planning system, where the communication infrastructure paradigm changed late in the project. When developing this system, we spent most time validating system-wide functionality. The model extensions allowed an easier change of the underlying communication paradigm and code generation supported realization of the different system representations.     

Distributed parameter system identification using finite element differential neural networks

Most of the previous work on identification involves systems described by ordinary differential equations (ODEs). Many industrial processes and physical phenomena, however, should be modeled using partial differential equations (PDEs) which offer both spatial and temporal distributions that are simply not available with ODE models. Systems described by a PDE belong to a class of system called distributed parameter system (DPS). This article presents a method for solving the problem of identification of uncertain DPSs using a differential neural network (DNN). The DPS, assumed to be described by a PDE, is approximated using the finite element method (FEM). The FEM discretizes the domain into a set of distributed and connected nodes, thereby, allowing a representation of the DPS in a finite number of ODEs. The proposed DNN follows the same interconnection structure of the FEM, thus allowing the DNN to identify the FEM approximation of the DPS in both 2D and 3D domains. Lyapunov's second method was used to derive adaptive learning laws for the proposed DNN structure. The identification algorithm, here developed in Nvidia's CUDA/C to reduce the execution time, runs mostly on the graphics processing unit (GPU). A physical experiment served to validate the 2D case. In the experiment, the DNN followed the trajectory of 57 markers that were placed on an undulating square piece of silk. The proposed DNN is compared against a method based on principal component analysis and an artificial neural network trained with group search optimization. In addition to the 2D case, a simulation validated the 3D case, where input data for the DNN was generated by solving a PDE with appropriate initial and boundary conditions over an unitary domain. Results show that the proposed FEM-based DNN approximates the dynamic behavior of both a real 2D and a simulated 3D system.