Ramdev Kanapady

Discontinuous Galerkin Methods for Timoshenko Beams

We devise a family of discontinuous Galerkin methods for the Timoshenko beam problem. Sufficient conditions for the existence and uniqueness of the approximation are given. The method allows arbitrary meshes and arbitrary polynomial degrees within the mesh, and hence is suitable for hp adaptivity. Numerical results showing optimal and exponential convergence are provided. These features of the method render it appealing for other problems in structure mechanics such as, plates, shells etc.

Localized prediction of continuous target variables using hierarchical clustering

We propose a novel technique for the efficient prediction of multiple continuous target variables from high-dimensional and heterogeneous data sets using a hierarchical clustering approach. The proposed approach consists of three phases applied recursively: partitioning, localization and prediction. In the partitioning step, similar target variables are grouped together by a clustering algorithm. In the localization step, a classification model is used to predict which group of target variables is of particular interest. If the identified group of target variables still contains a large number of target variables, the partitioning and localization steps are repeated recursively and the identified group is further split into subgroups with more similar target variables. When the number of target variables per identified subgroup is sufficiently small, the third step predicts target variables using localized prediction models built from only those data records that correspond to the particular subgroup. Experiments performed on the problem of damage prediction in complex mechanical structures indicate that our proposed hierarchical approach is computationally more efficient and more accurate than straightforward methods of predicting each target variable individually or simultaneously using global prediction models.

On a novel design of a new unified variational framework of discontinuous/continuous time operators of high order and equivalence

In this paper we present a novel design of a unified variational framework for both time continuous and discontinuous integration operators and also discuss in particular their equivalence via their respective spectral properties. As an added dimension, we also describe how the proposed approach enables the design of both time continuous/discontinuous high-order A -Stable schemes of order 2q, L-Stable schemes of order 2q- 1 and 2q- 2, and subsequently provide the requisite hierarchical computational structure of the resulting equations that is useful for time adaptive computations. In this regard, a new unified set of energy conserving and energy dissipating time discretized operators are described for both time continuous and discontinuous formulations for computational dynamics. Although the emphasis is placed on second-order systems, the developments also hold for first-order system representations.

Process modeling of composites by resin transfer molding: practical applications of sensitivity analysis for isothermal considerations

The resin transfer molding process for composites manufacturing consists of either of two considerations, namely, the fluid flow analysis through a porous fiber preform where the location of the flow front is of fundamental importance, and the combined flow/heat transfer/cure analysis. In this paper, the continuous sensitivity formulations are developed for the process modeling of composites manufactured by RTM to predict, analyze, and optimize the manufacturing process. Attention is focused here on developments for isothermal flow simulations, and various illustrative examples are presented for sensitivity analysis of practical applications which help serve as a design tool in the process modeling stages.

THE TIME DIMENSION AND A UNIFIED MATHEMATICAL FRAMEWORK FOR FIRST-ORDER PARABOLIC SYSTEMS

For the analysis of problems encompassing linear first-order parabolic systems involving the time dimension, the present exposition describes the evolution of and synthesis leading to a general unified mathematical framework and design of computational algorithms. In our previous efforts, various issues and the general classification and characterization of time-discretized operators were addressed, and the theoretical developments emanated from a generalized time-weighted residual philosophy which described the underlying consequences. Toward this end, in this article, for the first time, we provide alternative new perspectives and formalism via the notions of (1) the resulting size of the equation system and (2) the associated number of system solve(s). Although the time-weighted residual philosophy described an approach and the underlying consequences, from the new perspectives, the general design of computational algorithms is outlined in this article. A generalized stability and accuracy limitation theorem is also highlighted for linear transient algorithms encompassing first-order parabolic systems. Characterization as related to computational algorithms pertains to that which not only permits the general classification to be established but also provides the underlying basis for their subsequent design.

Effective localized regression for damage detection in large complex mechanical structures

In this paper, we propose a novel data mining technique for the efficient damage detection within the large-scale complex mechanical structures. Every mechanical structure is defined by the set of finite elements that are called structure elements. Large-scale complex structures may have extremely large number of structure elements, and predicting the failure in every single element using the original set of natural frequencies as features is exceptionally time-consuming task. Traditional data mining techniques simply predict failure in each structure element individually using global prediction models that are built considering all data records. In order to reduce the time complexity of these models, we propose a localized clustering-regression based approach that consists of two phases: (1) building a local cluster around a data record of interest and (2) predicting an intensity of damage only in those structure elements that correspond to data records from the built cluster. For each test data record, we first build a cluster of data records from training data around it. Then, for each data record that belongs to discovered cluster, we identify corresponding structure elements and we build a localized regression model for each of these structure elements. These regression models for specific structure elements are constructed using only a specific set of relevant natural frequencies and merely those data records that correspond to the failure of that structure element. Experiments performed on the problem of damage prediction in a large electric transmission tower frame indicate that the proposed localized clustering-regression based approach is significantly more accurate and more computationally efficient than our previous hierarchical clustering approach, as well as global prediction models.

A unified family of generalized integration operators [GInO] for non-linear structural dynamics: implementation aspects

Abstract The present paper proposes recent developments in theoretical and implementation aspects including parallel computations via a single analysis code of a unified family of generalized integration operators [GInO] in time with particular emphasis on non-linear structural dynamics. The focus of this research is on the implementation aspects including the development of coarse-grained parallel computational models for such generalized time integration operators that be can readily ported to a wide range of parallel architectures via a message-passing paradigm (using MPI) and domain decomposition techniques. The implementation aspects are first described followed by an evaluation for a range of problems which exhibit large deformation, elastic, elastic–plastic dynamic behavior. For geometric non-linearity a total Lagrangian formulation and for material non-linearity elasto-plastic formulations are employed. Serial and parallel performance issues on the SGI Origin 2000 system are discussed and analyzed for illustration for selected schemes. For illustration, particular forms of [GInO] are investigated and a complete development via a single analysis code is currently underway. Nevertheless, this is the first time that such a capability is plausible and the developments further enhance computational structural dynamics areas.

Local Discontinuous Galerkin Formulations for Heat Conduction Problems Involving High Gradients and Imperfect Contact Surfaces

A Local Discontinuous Galerkin (LDG) method is described here which provides a unied mathematical setting and framework for solving various kinds of heat conduction problems to include thermal contact conductance/resistance, sharp/high gradient problems and the like. For these applications, the LDG method does not require much modications to the basic formulation or the need to employ ad hoc approaches as with the Continuous Galerkin (CG) nite element methods. In this paper, we describe the LDG formulation for elliptic heat conduction problems which is then extended to parabolic problems. The advantages of the LDG method over the CG method are shown using two classes of problems|problems involving sharp/high gradients, and imperfect contact between surfaces. So far, interface/gap elements have been primarily used to model the imperfect contact between two surfaces to solve thermal contact resistance problems. The LDG method eliminates the use of interface/gap elements and provides a high degree of accuracy. It is further shown in the problems involving sharp/high gradients, that the LDG method is less expensive (requires less number of degrees of freedom) as compared to the CG method to capture the peak value of the gradient. Several illustrative 1-D/2-D applications highlight the eectiv eness of the present the LDG formulation.

Highly scalable parallel computational models for large-scale RTM process modeling simulations, Part 2: Parallel formulation theory and implementation

We highlight some key elements of the parallel formulation theory and implementational aspect of process modeling and manufacturing applications of composites with particular emphasis on resin transfer molding (RTM). The approaches for simulating process modeling and manufacturing applications of composites include (1) the traditional explicit control-volume finite-element (CV-FE) approach, and (2) a recently developed and new, implicit, pure finite-element (pure FE) approach. SGI Power Challenge and SGI Origin 2000, which are symmetric multiprocessor (SMP) computing platforms, are employed in this study. The issues in implementation and software development of these manufacturing process simulations are parallel algorithm development, data structures, and interprocessor communication strategies, with emphasis on performance and scalability on these symmetric multiprocessors. Fundamental concepts and characteristic features of the proposed scalable parallel algorithms are described and developed with theoretical analysis

High performance computing on a symmetric multiprocessor (SMP) environment for RTM process modeling of large complex structural geometries

Abstract The present paper discusses finite element computational schemes, data structures and interprocessor communication strategies for the implementation of advanced manufacturing simulations with particular emphasis on isothermal resin transfer molding (RTM) process manufacturing simulations on the symmetric multiprocessor (SGI Power Challenge). Thin shell composite mold configurations are used to illustrate the validity of the present implementation of a recently developed and new pure finite element implicit methodology in conjunction with a diagonal preconditioned conjugate gradient method for parallel computations including the process simulations techniques in a SGI Power Challenge node. The techniques developed are applied to large scale problems using a Power Challenge node to demonstrate the practical applicability.