Then, its generalization to non-proportional multiaxial fatigue problems is derived.
General eigenvalue problems are derived to solve the coupled governing equations.
Moreover, sufficient conditions expressed by linear programming problems are derived to design the required filters.
For this purpose, problems are derived based on an analysis of conventional BIM-based collaborative design.
Similarly to the abelian Ginzburg Landau model, the corresponding obstacle problems are derived.
At first, a 3D-to-2D general shell model based on a set of unit-cell problems is derived.
The problems are set in infinite dimension spaces, and the approximate problems are derived in finite dimension spaces.
Local closure problems are derived for the determination of the global stress contribution at the inter-region.
The governing equations and boundary conditions for static problems are derived in the unified formulation using the variational principle.
Finally, when there is only one degree of freedom for designing the mask coefficients, the globally optimal solutions of the unconstrained optimization problems are derived analytically.
