We present some novel equilibrium shapes of a clamped Euler beam (Elastica from now on) under uniformly distributed dead load orthogonal to the straight reference configuration. We characterize the properties of the minimizers of total energy, determine the corresponding Euler–Lagrange conditions and prove, by means of direct methods of calculus of variations, the existence of curled local minimizers. Moreover, we prove some sufficient conditions for stability and instability of solutions of the Euler–Lagrange, that can be applied to numerically found curled shapes.
Equilibria of a clamped Euler beam (Elastica) with distributed load: Large deformations / DELLA CORTE, Alessandro; Dell'Isola, Francesco; Esposito, Raffaele; Pulvirenti, Mario. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 27:8(2017), pp. 1391-1421. [10.1142/S0218202517500221]
Equilibria of a clamped Euler beam (Elastica) with distributed load: Large deformations
DELLA CORTE, ALESSANDRO;DELL'ISOLA, Francesco;PULVIRENTI, Mario
2017
Abstract
We present some novel equilibrium shapes of a clamped Euler beam (Elastica from now on) under uniformly distributed dead load orthogonal to the straight reference configuration. We characterize the properties of the minimizers of total energy, determine the corresponding Euler–Lagrange conditions and prove, by means of direct methods of calculus of variations, the existence of curled local minimizers. Moreover, we prove some sufficient conditions for stability and instability of solutions of the Euler–Lagrange, that can be applied to numerically found curled shapes.File | Dimensione | Formato | |
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