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- W75342710 abstract "the finite element analysis techniques are always based on an integral formulation. At the very minimum it will always be necessary to integrate at least an element square matrix. This means that every coefficient function in the matrix must be integrated. In the following sections various methods will be considered for evaluating the typical integrals that arise. Most simple finite element matrices for two-dimensional problems are based on the use of linear triangular or quadrilateral elements. Since a quadrilateral can be divided into two or more triangles, only exact integrals over arbitrary triangles will be considered here. Integrals over triangular elements commonly involve integrands of the form I=∫ A xmyn d x d y I = ∫ A x m y n d x d y (10.1) where A is the area of a typical triangle. When 0≤( m+n )≤2, the above integral can easily be expressed in closed form in terms of the spatial coordinates of the three corner points. For a right-handed coordinate system, the corners must be numbered in counter-clockwise order. In this case, the above integrals are given in Table 10.1. These integrals should be recognized as the area, and first and second moments of the area. If one had a volume of revolution that had a triangular cross-section in the - z plane, then one has I=∫ V ρf(ρ,z)dρ d z d φ=2π∫ A ρf(ρ,z)dρ d z I = ∫ V ρ f ( ρ , z ) d ρ d z d φ = 2 π ∫ A ρ f ( ρ , z ) d ρ d z so that similar expressions could be used to evaluate the volume integrals." @default.
- W75342710 created "2016-06-24" @default.
- W75342710 creator A5039380409 @default.
- W75342710 date "2005-01-01" @default.
- W75342710 modified "2023-09-27" @default.
- W75342710 title "Integration methods" @default.
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- W75342710 doi "https://doi.org/10.1016/b978-075066722-7/50041-2" @default.
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