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Download A Boundary Value Problem for Hypermon Genic Functions in by Yuying Q. PDF

By Yuying Q.

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2 Constant strain triangle Six noded and ten noded triangular elements (Fig. 3) are also used by the analysts. Six noded triangular element is known as Linear Strain Triangle (LST) or as Quadratic Displacement Triangle. Ten noded 3 3 8 6 7 5 9 4 1 (a) Fig. 3 2 1 10 4 6 5 2 (b) (a) Linear strain triangle (b) Quadratic strain triangle triangular elements are known as Quadratic Strain Triangles (QST) or Cubic Displacement Triangles. One can think of trying the use of still higher order triangular elements like Cubic Strain Triangles and Quartic Strain Triangles.

The modification required is, aij = a′i, ( j − i + 1) (ii) Partitioning of the Matrix For larger systems, even this method of storage may be inadequate. In such cases the partitioning of the matrix is made as shown in Fig. 10. Matrix Displacement Formulation 31 B I I II II III III IV IV Q P V V N VI VI R VII VII VIII VIII IX IX Fig. 10 Then only few of the triangular sub-matrices need to be stored in the computer core at a given time, while the remaining portions are kept in peripheral shortage like hard disk.

Explain the terms, ‘Anisotropic’, ‘Orthotropic’ and ‘Isotropic’ as applied to material properties. 6. Give constitutive laws for three dimensional problems of (i) orthotropic materials (ii) isotropic materials. 7. Explain the terms ‘Plane stress’ and ‘Plane strain’ problems. Give constitutive laws for these cases. 8. Explain the term ‘Axi-symmetric problems’ and give constitutive law for such problems. 1 INTRODUCTION Though mathematicians, physicists and stress analysts worked independently in the field of FEM, it is the matrix displacement formulation of the stress analysts which lead to fast development of FEM.

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