Application of generalized constraints in the stiffness method of structural analysis.

Greene, B. E.

doi:10.2514/3.3731

Cited by 13 publications

(1 citation statement)

References 4 publications

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“…In fact, the term GCs is not a new concept and it appeared in literature, such as a paper by Greene [5] in 1966. In the earlier The system output at the next step will be a function of the current output, as well as of the output with a time delay τ which is a positive integer.…”

Section: Mathematical Notation Of Generalized Constraintsmentioning

confidence: 99%

Generalized Constraints as A New Mathematical Problem in Artificial Intelligence: A Review and Perspective

Hu,

2020

Preprint

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In this comprehensive review, we describe a new mathematical problem in artificial intelligence (AI) from a mathematical modeling perspective, following the philosophy stated by Rudolf E. Kalman that "Once you get the physics right, the rest is mathematics". The new problem is called "Generalized Constraints (GCs)", and we adopt GCs as a general term to describe any type of prior information in modelings. To understand better about GCs to be a general problem, we compare them with the conventional constraints (CCs) and list their extra challenges over CCs. In the construction of AI machines, we basically encounter more often GCs for modeling, rather than CCs with well-defined forms. Furthermore, we discuss the ultimate goals of AI and redefine transparent, interpretable, and explainable AI in terms of comprehension levels about machines. We review the studies in relation to the GC problems although most of them do not take the notion of GCs. We demonstrate that if AI machines are simplified by a coupling with both knowledge-driven submodel and data-driven submodel, GCs will play a critical role in a knowledgedriven submodel as well as in the coupling form between the two submodels. Examples are given to show that the studies in view of a generalized constraint problem will help us perceive and explore novel subjects in AI, or even in mathematics, such as generalized constraint learning (GCL).

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Section: Mathematical Notation Of Generalized Constraintsmentioning

confidence: 99%

Generalized Constraints as A New Mathematical Problem in Artificial Intelligence: A Review and Perspective

Hu,

2020

Preprint

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A finite element model for shells based on the discrete Kirchhoff hypothesis

Weeks

1972

Numerical Meth Engineering

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SUMMARYA ring type finite element model based on the discrete Kirchhoff hypothesis is developed and its feasibility for use in shell analysis is illustrated by determining the linear axisymmetric deformation behaviour of a conical shell loaded by lateral pressure. The displacement field is represented by a linear function of the meridional co-ordinate. The effects of coupling between bending and extension are included and in this respect the analysis is an extension of earlier work by other investigators using this same model, where bending deformations only were considered. The results of the investigation indicate that the proposed model is capable of accurately described coupled bending and extension effects with a relatively small number of elements. In addition to the numerical results obtained several distinct advantages and disadvantages of this element are brought out. In particular, the element stiffness coefficients can be easily derived because of the simplicity of the assumed vector field. However, it appears that the price paid for such a simple vector field approximation is an undue amount of machine storage, even for a relatively small number of elements. Several suggestions are made for minimizing some of these difficulties.

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Error analysis of penalty function techniques for constraint definition in linear algebraic systems

Felippa¹

1977

Numerical Meth Engineering

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SUMMARYThe penalty function approach has been recently formalized as a general technique for adjoining constraint conditions to algebraic equation systems resulting from variational discretization of boundary value problems by finite difference or finite element techniques. This paper studies the numerical behaviour of the penalty function method for the special case of individual equation constraints imposed on a symmetric system of linear algebraic equations. Constraint representation and computational roundoff error components are distinguished and asymptotically characterized in terms of the penalty function weight coefficients. On the basis of this study, practical rules for the automatic assignment of values to those coefficients within the linear equation solver are proposed. Numerical problems encountered in the case of more general constraints are briefly discussed, and procedures for circumventing such difficulties are suggested.

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Application of generalized constraints in the stiffness method of structural analysis.

Cited by 13 publications

References 4 publications

Generalized Constraints as A New Mathematical Problem in Artificial Intelligence: A Review and Perspective

Generalized Constraints as A New Mathematical Problem in Artificial Intelligence: A Review and Perspective

A finite element model for shells based on the discrete Kirchhoff hypothesis

Error analysis of penalty function techniques for constraint definition in linear algebraic systems

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