{"paper":{"title":"A Riemannian Approach to Reduced Plate, Shell, and Rod Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math.FA"],"primary_cat":"math.DG","authors_text":"Jake P. Solomon, Raz Kupferman","submitted_at":"2012-01-17T17:29:01Z","abstract_excerpt":"We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not necessarily isometric $W^{1,2}$-immersion in $n$-dimensional Euclidean space. The equilibrium configuration is the immersion that minimizes the average discrepancy between the induced and intrinsic metrics. The dimensionally reduced limit theory views the elastic body as a $k$-dimensional Riemannian manifold along with an isometric $W^{2,2}$-immersion in $n$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3565","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}