In numerical integration to get
better result
we select n as
Answers
Answer:
here is your answer hope it helps ☺️
Step-by-step explanation:
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Numerical Integration
Numerical integration is always used: the first order elements use one point for volume strain and two points in each direction for deviatoric strain, while the second order elements allow three point or two point (reduced) integration of all components.
From: Structural Integrity Research of the Electric Power Research Institute, 1984
Related terms:
Energy EngineeringBoundary ConditionGaussIntegration MethodIntegration Point
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Improvements in the MATMOD Equations for Modeling Solute Effects and Yield-Surface Distortion
Gregory A. Henshall, ... Alan K. Miller, in Unified Constitutive Laws of Plastic Deformation, 1996
A Numerical Integration
Numerical integration of the equations described in this chapter is required to generate simulations of material response to a given loading history. It is important to consider the techniques of numerical integration for reasons of computational economy and compatibility with structural mechanics codes in which the constitutive equations may be employed.
The MATMOD-4V-DISTORTION equations are numerically integrated using the Gear Method for stiff differential equations. Such methods are necessary because of the inherent mathematical stiffness of any unified model, including MATMOD. The stiffness of these equations arises from the coupling of nonelastic and elastic strains to calculate the total strain, and the fact that
˙
ɛ
is a strong function of σ. Analogous
Answer:
In numerical integration to get a better result, we select n as large as possible.
Step-by-step explanation:
Romberg integration, which can produce reliable answers for a great deal fewer function evaluations, is a generalisation of the trapezoidal rule. The most effective numerical method of integration is known as Gaussian quadrature if the functions are known analytically rather than being tabulated at evenly spaced intervals. The midpoint rule, trapezoidal rule, and Simpson's rule are the methods for numerical integration that are most frequently utilised. While the trapezoidal rule uses trapezoidal approximations to estimate the definite integral, the midpoint rule uses rectangular regions to do so. Before attempting anything more complex, Simpson's rule, a form of numerical integration, should always be employed because it is significantly more accurate than the Trapezoidal rule.
Thus, it's always better to select n as large as possible for numerical integration.