A Newton Type Algorithm for Plastic Limit Analysis

Cover A Newton Type Algorithm for Plastic Limit Analysis
A Newton Type Algorithm for Plastic Limit Analysis
Veronique F Gaudrat
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Before going into the details of the algorithm and its implementation we will give some definitions and introduce the restricted objective function. Then a way to check the optimality will be presented.
III. L. Definition of the subspace and the restricted objective function We will use the notations of Overton in [6]. In the following the index j will represent (*\jiP)i'iJ = 1, . . . , A'^ - 1 and p = 1, 2. The objective function (1. 4) is written M (3. 1) h{xi) = Y, 0\t, {u)l where u € R^'^",
... A/ = 2 • (A' - 1)^ and e/u) = BjU, whereBj is a (4 x 2N^) matrix.
7 The active set at the point u is the set of triangles with zero-residuals : (3. 2) J(u) = {;||e»| = 0}, zind the active terms or residuals are ej(u) such that j G J{u). Let B be the matrix whose columns are the coefficient matrix of the active residuals: (3. 3) B= [B, Bj„... , Bj, ], where J(u) = {;i, j2, ... , Jp}, and let Z = Z{u), the matrix whose columns span the null space of B'. The matrix Z satisfies : (3. 4) 5'Z = 0, and (3.


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