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.     

Stochastic finite element analysis of shells

In the present paper the stochastic formulation of the triangular composite (TRIC) facet shell element is presented using the weighted integral and local average methods. The elastic modulus of the structure is considered to be a two-dimensional homogeneous stochastic field which is represented via the spectral representation method. As a result of the proposed derivation and the special features of the element, the stochastic stiffness matrix is calculated in terms of a minimum number of random variables of the stochastic field giving a cost-effective stochastic matrix. Under the assumption of a pre-specified power spectral density function of the stochastic field, it is possible to compute the response variability of the shell structure. Numerical tests are provided to demonstrate the applicability of the proposed methodologies.     

Nonlinear finite element analysis of shells: Part I. three-dimensional shells

A nonlinear finite element formulation is presented for the three-dimensional quasistatic analysis of shells which accounts for large strain and rotation effects, and accommodates a fairly general class of nonlinear, finite-deformation constitutive equations. Several features of the developments are noteworthy, namely: the extension of the selective integration procedure to the general nonlinear case which, in particular, facilitates the development of a ‘heterosis-type’ nonlinear shell element; the presentation of a nonlinear constitutive algorithm which is ‘incrementally objective’ for large rotation increments, and maintains the zero normal-stress condition in the rotating stress coordinate system; and a simple treatment of finite-rotational nodal degrees-of-freedom which precludes the appearance of zero-energy in-plane rotational modes. Numerical results indicate the good behavior of the elements studied.     

High-precision finite element analysis of cylindrical shells

This paper presents the finite element formulation to study the free vibration of cylindrical shells. The displacement function for the high-precision shell element with 16 degrees of freedom is approximated by a Hermitian polynomial of beam function type. The explicit formulation for the high-precision element is extremely efficient. For the purpose of comparison, the subject element is used to study the sample case of free vibration of a shell structure. The results are in good agreement with those published. The study shows that solution accuracy with fewer elements is assured and that accurate solutions are obtainable in the high-frequency range.     

Distributed finite element computations using object-oriented techniques

An object-oriented parallel finite element framework has been developed to facilitate rapid prototyping of a wide variety of parallel finite element computations. Parallel computing and object-oriented technologies are integrated to achieve efficiency in both computation and software development. The paper presents various reusable and extensible components that constitute the parallel finite element architecture.     

Integrated distributed sensing and active vibration suppression of flexible manipulators using distributed piezoelectrics

Structural oscillation of flexible robot manipulators would severely hamper their operation accuracy and precision. This article presents an integrated distributed sensor and active distributed vibration actuator design for elastic or flexible robot structures. The proposed distributed sensor and actuator is a layer, or multilayer of piezoelectric material directly attached on the flexible component needed to be monitored and controlled. The integrated piezoelectric sensor/actuator can monitor the oscillation as well as actively and directly constrain the undesirable oscillation of the flexible robot manipulators by direct/converse piezoelectric effects, respectively. A general theory on the distributed sensing and active vibration control using the piezoelectric elements is first proposed. An equivalent finite element formulation is also developed. A physical model with distributed sensor/actuator is tested in laboratory; and a finite element model with the piezoelectric actuator is simulated. The distributed sensing and control effectiveness are studied.     

Nonlinear finite element analysis of shells-part II. two-dimensional shells

A general nonlinear finite element formulation is given for two-dimensional problems. The formulation applies to the practically important cases of shells of revolution, tubes, rings, beams and frames. The approach is deduced from a corresponding three-dimensional formulation [4] and this enables a simplified implementation, especially with respect to constitutive software. Uniform reduced-integration Lagrange elements are employed and shown to be very effective for the class of problems considered.     

Building finite element analysis programs in distributed services environment

Traditional finite element analysis (FEA) programs are typically built as stand-alone desktop software. This paper describes an Internet-enabled framework that facilitates building a FEA program as distributed web services. The framework allows users easy access to the FEA core service and the analysis results by using a web browser or other application programs. In addition, the framework enables new as well as legacy codes to be incorporated from disparate sites in a dynamic and distributed manner. To provide flexible project management and data access, a database system is employed to store project-related information and selected analysis results. The prototype framework demonstrates that the Internet can potentially enhance the flexibility and extendibility of traditional FEA programs.     

Knowledge-based control for finite element analysis

This paper shows that control logic may be separated from analysis software and that a knowledge-based expert system can use this logic to perform interactive computation. Heuristics that control a simple interactive finite element analysis program are represented using a rule-based format and are used by a goal-driven logic processor to invoke analysis activity.Traditional algorithm-oriented control and the proposed knowledge-based control are compared in a simple displacement computation scenario to identify the advantages/disadvantages of the two approaches. General activities and constraints, practical methods of reasoning and representation, and knowledge-based expert systems are discussed with emphasis on applications to interactive finite element analysis.An analysis control expert system has been developed for use in the numerical analysis of two-dimensional linear problems in solid and structural mechanics. An example problem is used to clarify the methods used to direct activity and to identify the problems associated with conditional task processing for interactive analysis.The main difference between the analysis program described in this paper and conventional analysis programs is related to the control architecture. The general conclusion of this paper is that knowledge-based control is more effective and flexible than algorithm-oriented control.     

A hybrid strain technique for finite element analysis of plates and shells

A specialization of the Hu-Washizu [1] functional wherein strains and displacements are taken as independent variables is employed in the formulation of ‘hybrid’ elements. Both the strains and displacements are independently interpolated with the strains being eliminated at the element level, leaving displacement variables only to be assembled into the global system of equations. This distinguishes such elements as ‘hybrid’, in contrast to ‘mixed’ wherein the global system of equations contains all the discretized variables. Applications including ‘thick’ plate and shell elements are considered. In many applications the hybrid strain technique appears more natural than the hybrid stress technique since stress discontinuities are accommodated quite conveniently.     

Distributed parameter system optimum control design via finite element discretization

The problem of designing an optimum distributed parameter system is considered. Fundamental concepts pertaining to the solution of optimum controls for distributed parameter systems by finite element methods are devised. It is demonstrated that methods can readily be applied to solve problems involving nonlinear Neumann boundary conditions.     

Optimum structural design with parallel finite element analysis

Structural analysis is an important part of the optimum structural design process. Therefore, extra effort should be devoted to make this part as efficient as possible. Since finite element analysis is the most powerful and widely used tool in the structural analysis field, in this paper a new method for structural optimization by parallel finite element method is presented. This method divides the original structure into several substructures and assigns each substructure to one processor. Each processor handles its finite element calculation independently with limited communication between processors. Some numerical examples on the Cray X-MP multiprocessor system with their obtained speedups are presented.     

Real-time finite element structural analysis in augmented reality

Conventional finite element analysis (FEA) is usually carried out in offsite and virtual environments, i.e., computer-generated graphics, which does not promote a user’s perception and interaction, and limits its applications. With the purpose of enhancing structural analysis with augmented reality (AR) technologies, the paper presents a system which integrates sensor measurement and real-time FEA simulation into an AR-based environment. By incorporating scientific visualization technologies, this system superimposes FEA results directly on real-world objects, and provides intuitive interfaces for enhanced data exploration. A wireless sensor network has been integrated into the system to acquire spatially distributed loads, and a method to register the sensors onsite has been developed. Real-time FEA methods are employed to generate fast solutions in response to load variations. As a case study, this system is applied to monitor the stresses of a step ladder under actual loading conditions. The relationships among accuracy, mesh resolution and frame rate are investigated.     

An elastoplastic cracked-beam finite element for structural analysis

A finite element model has been developed in this paper to analyse statically indeterminate skeletal cracked structures. The model is based on elastic-plastic fracture mechanics techniques in order to consider the crack tip plasticity in the analysis. Stiffness matrices for single-edge and double-edge cracked structural elements have been derived using transfer matrix theory. These matrices take into account the effects of axial, flexural and shear deformations due to crack presence. The present model has been applied to investigate the effects of crack size, structure cross-section depth and crack tip plasticity on the redistribution of internal forces in structures. Hence, this analysis can be employed to identify the overstressed regions in cracked structures.     

Nonlinear finite element analysis of reinforced concrete plates and shells under monotonic loading

Plane stress constitutive models are proposed for the nonlinear finite element analysis of reinforced concrete structures under monotonic loading. An elastic strain hardening plastic stress-strain relationship with a nonassociated flow rule is used to model concrete in the compression dominating region and an elastic brittle fracture behavior is assumed for concrete in the tension dominating area. After cracking takes place, the smeared cracked approach together with the rotating crack concept is employed. The steel is modeled by an idealized bilinear curve identical in tension and compressions. Via a layered approach, these material models are further extended to model the flexural behavior of reinforced concrete plates and shells. These material models have been tested against experimental data and good agreement has been obtained.     

An error estimation method in finite element structural analysis

In the paper a new interpretation of the finite element approach is described and illustrated numerically. The conventional shape functions of the displacement—and stress—type finite element models are treated as constraints imposed on the continuous medium considered. This enables a consistent error estimation analysis based on a concept of so-called reaction forces and deformation incompatibilities.     

An adaptive finite element technique for structural dynamic analysis

An adaptive finite element discretization technique, which utilizes specially derived Ritz vectors, is presented for solving structural dynamics problems. The special Ritz vectors are applied as the bases of transformation in geometric coordinates for mode superposition dynamic analysis. To capture the low frequency response and the high frequency response using multigrid principles, a hierarchical formulation for the formation of the coefficient matrices is proposed and it is utilized in the framework of the adaptive h-refinement. Assuming that the solution can be resolved into a set of orthogonal vectors and the refined mesh which passes the refinement criteria for all the vectors can satisfy the refinement criteria for the solution, the Ritz vectors are used as sources to discretize the continuous spatial domain. An a posteriori energy norm of residual error serves as the error measure. Finally, the performance and the efficiency of the proposed technique is demonstrated by solving several examples.     

NASTRAN—a finite element program for structural analysis

Nastran has been designed for NASA to handle large problems with any degrees of freedom. The user can either instruct the executive system to perform the operations he wishes or he can make use of one of twelve rigid formats, each of which performs a particular analysis. Lloyd's Register are at present evaluating Nastran. Container ships and supertankers pose new structural problems whose solution may require 10 000–15 000 degrees of freedom.     

Object oriented implementation of distributed finite element analysis in .NET

The paper describes a detailed study into the object-oriented implementation of distributed finite element analysis on desktop computers using the .NET framework. The software design aspects are described in some detail for both direct and iterative solution algorithms. The use of interfaces played an important role in the software design. This, together with the .NET framework, enabled remote objects to be implemented in a relatively seamless fashion. The solution routines were “blind” to whether the objects were local or remote. Numerical tests were carried out and reasonable speed-up was achieved, particularly for direct solution methods. It is concluded that .NET provides a viable framework for implementing distributed computing on networks of personal computers.     

分析结构力学与有限元

分析力学历来是在动力学范围内论述的,结构力学与最优控制模拟关系的共同基础就是分析力学．这表明在结构力学与最优控制理论的架构内也应有分析力学的整套理论．本文就结构力学讲述分析力学,称分析结构力学．保守体系可用Hamilton体系的方法描述,其特点是保辛．保辛给出保守体系结构最重要的特性．有限元法是从结构力学发展的,有限元的单元刚度阵应保持对称性,其实这就是保辛．根据区段单元变形能只与其两端位移有关,就可通过数学分析得到Lagrange括号与Poisson括号,展示了其辛对偶体系、正则方程、正则变换等的内容．