By Houben H., Boubekeur S.
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Extra info for Compressed Earth Blocks. Standards
10 compares the logarithm of the relative error in t~e Gauss and the singular integration methods for two terms of the matrix Ife when a is equal to 1. The analysis of the results given by this figure shows that the accuracy given by 2 integration points is always insufficient For a higher number of integration points (NIP), the accuracy improves and the singular integration method gives bener results than the Gauss integration method. e 6 4 8 NIP -1 -2 -3 -4 -5. 10 The comparison of the integration methods for a three node element  leads to similar conclusion.
3. 32) has p integration points which compute the integral exactly if the degree of f(x) is equal or lower than (2p - 1). 2 [IOJ. 96884798 Note: Numbers are to be multiplied by the power of 10 in parentheses. Introduction In this section, the results given by different integration methods will be compared with those given by Gauss. The fIrst example is simple to make an analytical computation possible. J@. 12) will be computed. 12). 3, considering that the domain is isotropic (K = Kx = Ky). 33) using 2, 4, 6 and 10 integration points.
7. 2) giving the components of the linear system. To use this integration method, the collocation point i must be located on an element other than the one under consideration. If this condition is not verified, one needs to apply singular numerical integration methods to compute these two integrals. These methods will be developed in the following sections. The developments presented up to now regarding the shape functions, the jacobian and the components of the outward normal vector will also be applied for the study of the singular integrals.