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• Numerical experiments in finite element grid optimization by direct energy search

  C. Felippa

  Applied Mathematical Modelling (1977). Vol. 1 (5), pp. 239-244

  
  

  Abstract

  A series of numerical experiments is conducted to assess the feasibility and practical value of finite element grid optimization based on direct minimization of the total potential energy of the discrete model with respect to the node locations. An implementation relying upon non-linear programming techniques is found to be numerically reliable and to lead to improved grids in accord with engineering intuition. This rigorous approach is hampered, however, by the excessive computational effort required by the energy minimization process. A combination of related techniques is therefore proposed to make dynamic node distribution a useful tool within the framework of large-scale finite element analysis. The combined strategy involves use of substructuring methods, application of a local energy-balancing optimality criterion for fast node distribution, and automatic refinement of previously-improved coarse grids.

  Abstract
  A series of numerical experiments is conducted to assess the feasibility and practical value of finite element grid optimization based on direct minimization of the total [...]

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• Iterative solutions for improving penalty function solutions of algebraic systems

  C. Felippa

  International Journal for Numerical Methods in Engineering (1978). Vol. 12 (5), pp. 821-836

  
  

  Abstract

  The standard implementation of the penalty function approach for the treatment of general constraint conditions in discrete systems of equations often leads to computational difficulties as the penalty weights are increased to meet constraint satisfaction tolerances. A family of iterative procedures that converges to the constrained solution for fixed weights is presented. For a discrete mechanical system, these procedures can be physically interpreted as an equilibrium iteration resulting from the appearance of corrective force patterns at the nodes of ‘constraint members’ of constant stiffness. Three forms of the iteration algorithm are studied in detail. Convergence conditions are established and the computational error propagation behaviour of the three forms is analysed. The conclusions are verified by numerical experiments on a model problem. Finally, practical guidelines concerning the implementation of the corrective process in large-scale finite element codes are offered.

  Abstract
  The standard implementation of the penalty function approach for the treatment of general constraint conditions in discrete systems of equations often leads to computational [...]

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• Computational Aspects of Time Integration Procedures in Structural Dynamics---Part 2: Error Propagation

  K. Park, C. Felippa

  Journal of Applied Mechanics (1978). Vol. 45 (3), pp. 603-611

  
  

  Abstract

  The propagation of computational error in the direct time integration of the equations of structural dynamics is investigated. Asymptotic error propagation equations corresponding to the computational paths presented in Part 1 are derived and verified by means of numerical experiments. It is shown that there exists an implementation form that achieves optimum error control when used in conjunction with one-derivative methods. No such form is found for two-derivative methods. A numerical beating phenomenon is observed for certain implementations of the average acceleration method and the trapezoidal rule, which from an error propagation standpoint, is highly undesirable.

  Abstract
  The propagation of computational error in the direct time integration of the equations of structural dynamics is investigated. Asymptotic error propagation equations corresponding [...]

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• Computational Aspects of Time Integration Procedures in Structural Dynamics---Part 1: Implementation

  C. Felippa, K. Park

  Journal of Applied Mechanics (1978). Vol. 45 (3), pp. 595-602

  
  

  Abstract

  A unified approach for the implementation of direct time integration procedures in structural dynamics is presented. Two key performance assessment factors are considered, viz. , computational effort and error propagation. It is shown that these factors are strongly affected by details in the reduction of the second-order equations of motion to a system of first-order equations, and by the computational path followed at each time step. This paper is primarily devoted to the study of the organization of the computational process. Specific implementation forms derivable from the unified approach are studied in detail, and rated accordingly.

  Abstract
  A unified approach for the implementation of direct time integration procedures in structural dynamics is presented. Two key performance assessment factors are considered, [...]

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• Direct integration methods in nonlinear structural dynamics

  C. Felippa, K. Park

  Computer Methods in Applied Mechanics and Engineering (1979). Vol. 17-18, pp. 277-313

  
  

  Abstract

  This paper reviews some recent developments in direct time integration methods for nonlinear structural dynamics. The developments pertain to the use of linear multistep difference operators in conjunction with the pseudo-force approach. The paper is organized into three main sections. An introductory section provides an overview of the transient response analysis problem. A section on computational aspects deals with the organization of the numerical calculations; this material is largely based on a recent detailed study of linear dynamic calculations [1–2]. A section on integration methods highlights algorithmic aspects that impact the selection of integrator for nonlinear problems and discusses adaptive analysis features such as stepsize control and implicit matrix scaling techniques. An appendix section outlines the functional organization of modular “integration driving” software.

  Abstract
  This paper reviews some recent developments in direct time integration methods for nonlinear structural dynamics. The developments pertain to the use of linear multistep difference [...]

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• A contour-line printplotter for finite element work

  C. Felippa

  Advances in Engineering Software (1979). Vol. 1 (2), pp. 51-60

  
  

  Abstract

  A Fortran subroutine for producing countour line printplots of functions defined at the nodes of an arbitrary two-dimensional finite element mesh is presented. This display technique is useful for quick inspection of analysis results and as guide for downstream use of more sophisticated graphics equipment.

  Abstract
  A Fortran subroutine for producing countour line printplots of functions defined at the nodes of an arbitrary two-dimensional finite element mesh is presented. This display [...]

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• Symposium on future trends in computerized structural analysis and synthesis

  C. Felippa

  Applied Mathematical Modelling (1979). Vol. 3 (2), pp. 1

  
  

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• Database Management in Scientific Computing Part I: General Description

  C. Felippa

  Computers and Structures (1980). Vol. 12, pp. 131-146

  
  

  Abstract

  Techniques for generalized data management are gradually making inroads in scientific computing in general and computerized engineering analysis in particular. This development parallels in many ways the rapid acceptance of the centralized database concept in business-oriented processing during the 1970s. Scientific database manipulation systems face, however, a specialized general features of scientific data management from a functional standpoint. Special emphasis is given to the discussion of trends in the development of large-scale programs, as well as the assembly of database-linked program networks for engineering analysis. 

  Abstract
  Techniques for generalized data management are gradually making inroads in scientific computing in general and computerized engineering analysis in particular. This development [...]

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• Axisymmetric free vibration of a submerged spherical shell

  C. Felippa, T. Geers

  Journal of the Acoustical Society of America (1980). Vol. 67 (5), pp. 1427-1465

  
  

  Abstract

  Previous studies have produced only partial solutions for this classical configuration. It is shown here how complete solutions are readily obtained from simple polynomial expressions. Numerical results in graphical form are given for a steel shell submerged in water as functions of a parameter related to the shell's thickness-to-radius ratio. It is found that descriptions based upon added-mass and added-damping perturbations of the shell's in vacuo free-vibration characteristics can be misleading.

  Abstract
  Previous studies have produced only partial solutions for this classical configuration. It is shown here how complete solutions are readily obtained from simple polynomial [...]

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• Database management in scientific computing—II. Data structures and program architecture

  C. Felippa

  Computers and Structures (1980). Vol. 12 (1), pp. 131-145

  
  

  Abstract

  The second of a three-part paper on scientific database management prepares the ground for the operational description of a multilevel data management system in Part III. Following a detailed categorization of data and storage structures, principles of program architecture deemed necessary to make most efficient use of centralized data management techniques are discussed. General operational requirements of data management systems are presented, and the notion of activity levels introduced. This part closes with a brief review of the evolution of data management techniques in the context of computerized structural analysis.

  Abstract
  The second of a three-part paper on scientific database management prepares the ground for the operational description of a multilevel data management system in Part III. [...]

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