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Engineering applications of numerical integration in stiffness methods.
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This article is published in AIAA Journal.The article was published on 1966-11-01. It has received 212 citations till now. The article focuses on the topics: Numerical integration & Stiffness.read more
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A proposed standard set of problems to test finite element accuracy
TL;DR: A proposed standard set of test problems is described and applied to representative quadrilateral plate and solid brick finite elements, some of which have become de facto standards for comparing the accuracy of finite elements.
Journal ArticleDOI
Efficient quadrature for NURBS-based isogeometric analysis
TL;DR: In this article, the half-point rule is introduced for NURBS-based isogeometric analysis, indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom, or equivalently half the basis functions of the space under consideration.
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Elasto‐plastic stress analysis. A generalization for various contitutive relations including strain softening
G. C. Nayak,O. C. Zienkiewicz +1 more
TL;DR: In this article, the authors discuss several similar strategies for solving the problem of elas-to-plastic problems in the context of a general formulation, which includes ASSOCIATED and Non-Associated PLASTIC RELATIONS and StRAIN HARDENING as well as STRAIN SOFTENING.
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Gaussian quadrature formulas for triangles
TL;DR: In this article, several formulas for the numerical integration of a function over a triangular area are presented, which are of the Gaussian type and are fully symmetric with respect to the three vertices of the triangle.
Journal ArticleDOI
Curved, isoparametric, “quadrilateral” elements for finite element analysis
TL;DR: In this article, the theory of a new family of isoparametric elements for use in two-dimensional situations is described, and examples illustrating the accuracy improvement are included in the paper.
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Vibration of a 45 deg right triangular cantilever plate by a gridwork method
TL;DR: A free vibration solution for a 45° right triangular cantilever plate is given in this article, where a grid work analogy for plate bending is derived and applied to obtain the first 10 natural frequencies and mode shapes.