Taniq develops technology for manufacturers of cord-reinforced rubber products t o improve their product performance and production process through product redesign and supply of software and production equipment. Taniq's technology is used for products ranging from straight large-bore hoses (0600 [mm]) to small bellowed expansion joints (0 < 100 [mm]). The current structural analysis used at Taniq is only able to predict fibre stresses of single-layered products in basic load cases. As many products require local reinforcements and/or multiple fibre layers this basic structural analysis is not proficient. Therefore these products are currently designed by trial-and-error. It is of importance to gain insights in the complete stress state throughout the product in any load case to facilitate a more efficient design process. This stress state can be used for static and dynamic strength predictions, and f o r the development of design guidelines for future products.

This thesis demonstrated how the Newton and BFGS algorithm could be used to solve the standard VGM relations and least-squares formulation respectively, for arbitrary forms of the _ parameter, including nonlinear _ s, appearing in the VMM. The proposed procedure were also shown to be able to handle arbitrary projectors that are compatible with the VGM. When applied to the advection-di_usion equation, Burgers' equation and Stokes equations the algorithms always reached the speci_ed stopping criteria and did not exceed the maximum alloted iterations. Additionally the increase in computational e_ort required was shown to be limited. However, it was shown that the Newton procedure for the VGM could not be used in cases where the local VGM residuals had varying signs. In that case the BFGS and least-squares VGM were successful. Application of the proposed procedures to di_erent SGS models showed that nonlinear models tended to outperform linear models in terms of the L2 and projected error. It was also shown that the parametrization of an SGS model can greatly inuence how well the VGM will be able to optimize its coe_cients.