By Daniel Priour
This e-book absolutely describes a finite point approach for netting. That describes the relation among forces and deformation of the netting. That takes into consideration forces a result of wire elasticity, the hydrodynamic forces, the capture impact, the mesh establishing stiffness. This e-book is split in five components. the 1st part includes creation at the finite point approach, the second one half is ready equilibrium calculation, the 3rd offers a triangular aspect for netting, the fourth and 5th are for cable and node point. The 6th offers few validation cases.
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Additional info for A Finite Element Method for Netting: Application to fish cages and fishing gear
33) The principle of virtual work implies that the external work equals the internal work, since the forces represent the tension in the twines. 42) | ∂|V | The derivatives ∂|U ∂ x1 ... ∂z3 can be calculated, as the equations relating to U , V and X i , Yi , Z i have already been described. 45) The Newton-Raphson method, described earlier, requires the calculation of the stiffness matrix, which is calculated from the derivatives of effort with respect to the positions of the vertices of the triangular element.
There are relations between the mesh coordinates and the twine coordinates, the bases of which are noted in Fig. 8b and c. 9) This leads to: u+v 2 v−u V= 2 U= u, v: mesh coordinates base, U, V: twine coordinates base. 11) 34 4 The Triangular Finite Element for Netting -60 10 10 -60 10 -60 -60 10 -60 -60 -60 -60 Fig. 7 Two deformations of the same structure. The twines coordinates of vertices remain constant. The twines coordinates of three vertices are noted. The dot is the origin of twines numbering.
4 Twine Flexionin Netting Plane The resistance to twine bending in the plane of the net is also called the mesh opening stiffness (Fig. 13). In a first approximation, this stiffness is neglected, but the use of steeper nets makes it necessary to take this mechanical phenomenon into account in numerical models. Currently, only [15, 12] and the present model take this mesh opening stiffness into account. In the present model, the half angle (α) between the twine vectors (U and V) could lead to a couple between twine vectors (U and V).