The paper is centered on an iterative procedure, which can be adopted for the structural analysis of elastic frames subjected to large displacements. In consequence, the equilibrium equations are written by considering the deformed configuration. The algorithm is based on the finite element method and essentially requires the solution of a sequence of linear elastic problems. At each iteration, the nodal displacements are updated according to the small displacement theory. Thus, the numerical approach discussed here makes use of the usual tools, which are typical of a simple linear elastic analysis. More specifically, after a preliminary analysis that is performed by considering a given set of external loads and by imposing equilibrium with respect to the initial configuration, the actual curvatures of the beam elements are determined and convenient equivalent nodal loads are computed. Next, a new mesh is generated in order to account for the deformed configuration of the framed structure and further incremental displacements are found by applying a set of nodal loads, which represent the difference between the given loads and the loads determined at the end of the previous analysis. The process continues until a convenient measure of the discrepancy between the displacements computed at the last iteration and the displacements estimated at the previous iteration is below a given tolerance. To this aim, it is possible to compare the Euclidean norms of the displacement vectors evaluated at two subsequent iterations. Some preliminary numerical tests on simple plane systems show that the approach presented in this paper does give results, which are consistent with analytical and/or experimental solutions.

### A simple approach to the large-displacement analysis of elastic framed structures

#### Abstract

The paper is centered on an iterative procedure, which can be adopted for the structural analysis of elastic frames subjected to large displacements. In consequence, the equilibrium equations are written by considering the deformed configuration. The algorithm is based on the finite element method and essentially requires the solution of a sequence of linear elastic problems. At each iteration, the nodal displacements are updated according to the small displacement theory. Thus, the numerical approach discussed here makes use of the usual tools, which are typical of a simple linear elastic analysis. More specifically, after a preliminary analysis that is performed by considering a given set of external loads and by imposing equilibrium with respect to the initial configuration, the actual curvatures of the beam elements are determined and convenient equivalent nodal loads are computed. Next, a new mesh is generated in order to account for the deformed configuration of the framed structure and further incremental displacements are found by applying a set of nodal loads, which represent the difference between the given loads and the loads determined at the end of the previous analysis. The process continues until a convenient measure of the discrepancy between the displacements computed at the last iteration and the displacements estimated at the previous iteration is below a given tolerance. To this aim, it is possible to compare the Euclidean norms of the displacement vectors evaluated at two subsequent iterations. Some preliminary numerical tests on simple plane systems show that the approach presented in this paper does give results, which are consistent with analytical and/or experimental solutions.
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2017
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11368/2915458`