John O. Dow

Error estimation procedure for plate bending elements

The elemental errors are identified through the use of an element formulation procedure based on physically interpretable strain-gradient interpolation functions. The use of this notation allows these errors to be eliminated using rational arguments. The discretization errors are identified by comparing the finite-element solution to a smoothed superconvergent solution. The errors thus identified are used to guide an adaptive mesh refinement procedure that produces improved results

Expert systems, neural networks and artificial intelligence applications in commercial building HVAC operations

Abstract For several years researchers at the JCEM have sought ways to apply various artificial intelligence methods to commercial building HVAC operations. This paper, based on two earlier articles, reports on some of the key results of work at Colorado. Expert system enhanced with neural networks trained by historical building data appear to be particularly promising for efficient and semi-automatic supervision of HVAC systems for commercial buildings. It appears that the over reliance on logic associated with expert systems alone can be reduced with a bettwe results neurl networks.

Validation of a finite element error estimator

the smoothed solution against which the finite element stresses are compared is based on a reformulation of the finite difference method that permits irregular meshes and complex boundary conditions to be analyzed

Nonstandard Finite Difference Models

Purpose of Lesson To present nonstandard modeling capabilities for the finite difference method that have been developed as a result of the use of strain gradient notation and the new boundary condition models.

Submodeling approach to adaptive mesh refinement

A submodeling approach for adaptively refining stress concentrations has been developed. The stress concentrations are separated from the remainder of the problem one at time by defining internal boundaries in terms of elemental error measures. The fact that the effects of the remainder of the problem are satisfactorily included in the subproblem by interpolating the displacements across the internal boundary is indicated by the accuracy of the results. The adaptive refinement is terminated when the maximum elemental error reaches a predetermined value. This contrasts to some approaches where a global error measure is used to terminate the analysis. The use of the elemental error measure to stop the analysis removes the effect of the far-field elements from the assessment of the accuracy of the results at the stress concentration. The accuracy of the analysis in the region of interest is used to terminate the analysis. The adaptive refinement of a submodel containing a stress concentration allows the computational resources to be focused on the regions of the problem where they can best be utilized. For instance, if a problem has several high-stress regions, each one can be treated separately and in detail. The 5% elemental error criterion used here to define both the internal boundary and to terminate the analysis was chosen arbitrarily. Previous experience had shown that this value would produce well-converged results for the example problems solved here. Thus, a valuable area of future resarch would be to determine a process for identifying the criteria that would produce the desired mix between accuracy and efficiency for general problems.

Lesson 2 – Elements of the Calculus of Variations

Purpose of Lesson To introduce the concepts or elements of the calculus of variations and use them to develop the necessary conditions for minimizing functionals.

Error Identification in Individual Finite Elements: A Path to the Integration of Continuum and Computational Mechanics

A procedure for extracting equivalent continuum parameters, i.e., (EI) equiv , from skeletal structures has been extended. This procedure which exploits a direct symbolic relationship between the approximation polynomials used in computational mechanics and the equations of continuum mechanics has been used to unify and improve the finite element and finite difference methods. This, in turn, allowed error measures to be put on a solid theoretical foundation and has led to the development of new methods of error identification.

ON A FOUR-NODE QUADRILATERAL PLATE FOR LAMINATED COMPOSITES

AN ASSESSMENT OF THE EFFICIENCY AND CONVERGENCE CHARACTERISTICS OF A FOUR-NODE QUADRILATERAL PLATE FINITE ELEMENT IN THE ANALYSIS OF LAMINATED COMPOSITES IS PERFORMED. THE ELEMENT, WHICH IS SUITABLE FOR GLOBAL RE-SPONSE ANALYSIS, IS DEVELOPED IN THE FRAMEWORK OF THE STRAIN GRADIENT NOTATION SUCH THAT ITS MODELING CAPABILITIES AS WELL AS MODELING DEFICIENCIES CAN BE PHYSICALLY INTERPRETED BY THE ANALYST DURING THE FORMULATION PROCESS. THUS, SHEAR LOCKING TYPICALLY ENCOUNTERED IN FOUR-NODED PLATE ELEMENTS IS IDENTIFIED AS CAUSED BY SPURIOUS TERMS WHICH APPEAR IN THE SHEAR STRAIN POLYNOMIAL EXPANSIONS. THESE IDENTIFIED SPURIOUS TERMS ARE REMOVED A PRIORI SUCH THAT SHEAR LOCKING DOES NOT OCCUR DURING NUMERICAL ANALYSIS AND NUMERICAL REMEDIES DO NOT NEED TO BE APPLIED. STRESS SOLUTIONS FOR DIFFERENT LAMINATED PLATES ARE PRESENTED TO DEMONSTRATE THAT THE CORRECTED MODEL CONVERGES WELL TO REFERENCE SOLUTIONS.

Lesson 19 – A Theoretical Foundation for Pointwise Evaluation Measures

Purpose of Lesson To provide a theoretical foundation for two types of pointwise evaluation measures: (1) those based on stress differences between the smoothed and the finite element stresses (see Lesson 18 ) and (2) those based on residuals contained in the augmented solution.

Strain Gradient Representation of Discrete Structures

Purpose of Lesson To present procedures for identifying and utilizing linearly independent sets of strain gradient quantities that a two-dimensional truss is capable of representing as a way to highlight the role of individual strain states as generalized coordinates.