{"ID":2824472,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.23695","arxiv_id":"2512.23695","title":"A dimension reduction procedure for the selection of Two-spring lattice-spring topologies with minimal fabrication cost and required weighted force-resistance performance","abstract":"Starting from a problem in elastoplasticity, we consider an optimization problem $C(c_1,c_2)=c_1+c_2\\to \\min$ under constraints $F_R^k(c_1,c_2)=a\\cdot F^k(c_1,c_2)+b\\cdot R^k(c_1,c_2)\\ge 1$ and $F^k(c_1,c_2)\\ge 1$, where both $F^k$ and $R^k$ non-linear, $a,b$ are constants, and $i\\in\\{1,2\\}$ is an index. For each $(a,b)$ we determine which of the two values of $i\\in\\{1,2\\}$ leads to the smaller minimum of the optimization problem. This way we obtain an interesting curve bounding the region where $k=1$ outperforms $k=2$.","short_abstract":"Starting from a problem in elastoplasticity, we consider an optimization problem $C(c_1,c_2)=c_1+c_2\\to \\min$ under constraints $F_R^k(c_1,c_2)=a\\cdot F^k(c_1,c_2)+b\\cdot R^k(c_1,c_2)\\ge 1$ and $F^k(c_1,c_2)\\ge 1$, where both $F^k$ and $R^k$ non-linear, $a,b$ are constants, and $i\\in\\{1,2\\}$ is an index. For each $(a,b...","url_abs":"https://arxiv.org/abs/2512.23695","url_pdf":"https://arxiv.org/pdf/2512.23695v1","authors":"[\"Egor Makarenkov\"]","published":"2025-12-29T18:52:36Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}