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AAU Dept anisotropy beam bioprobes boundary conditions cantilever CENTER FOR APPLIED corresponding crack direction crack-tip curves DANISH CENTER Denmark Department of Mechanical design variable dihedral angle divergence boundary divergence domain double eigenvalue DTU Dept DTU Institute effective plastic strain eigenfunctions eigenvalue problem eigenvalue sensitivity energy density equation fiber finite element analysis fixed basis function flutter boundary fracture graded layer hole Informatics and Mathematical initial crack Institute of Mechanical isotropic Keldysh chain kinematic constraints load MATHEMATICS AND MECHANICS matrix Mechanical Engineering modulus moving boundary multi parameter theory Niordson numerical obtained optimal design orientational design orthotropic materials particles Pauli Pedersen piezoresistive material plane strain plastic flow plate point pn Poisson's ratio ratio reference problem relative density sensitivity analysis sensitivity problem shape sensitivity shown in figure single parameter theory sintering Solid Mechanics solution stiffness Technical University thickness Tvergaard University of Denmark values vector yield stress zero eigenvalue