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A three-dimensional finite-strain rod model. II. Computational aspects. (English) Zbl 0608.73070
This second part is concerned with the variational formulation and numerical implementation of a three-dimensional finite-strain rod model considered in part I of the paper [ibid. 49, 55-70 (1985; Zbl 0583.73037)]. This model is a reparametrization of an extension to the classical Kirchhoff-Love model including finite extension and shearing of the rod, and avoiding the use of Euler angles.
The basic features of the rod model employed in this paper are summarized in section 2. In section 3, the authors consider the appropriate definition of admissible variations and the consistent linearization of the strain measures. Weak forms of balance equations are derived in section 4 for the static case. A consistent linearization allows to define a tangent operator which is nonsymmetric except at equilibrium. The finite element formulation of the previous variational equations is studied in section 5. The authors make use of uniformly reduced integration on the pure displacement weak form to avoid shear locking. Next, it is shown in section 6 that nonconservative loading can be accomodated within the present formulation. Finally, in section 7, a series of numerical simulations illustrates the performance of the formulation: successively, the authors consider a pure bending of a cantilever beam, a cantilever beam subject to follower end load, a clamped-hinged deep circular arch subject to point load, the buckling of a hinged right-angle frame under both fixed and follower point load, a cantilever 45-degree bend subject to fixed and follower end load, the lateral buckling of a cantilever right-angle frame under end loads, and the lateral buckling of a hinged right-angle frame for which a complete post-buckling diagram is given.
This is a very nice paper, both for the contents and the form.
Reviewer: M.Bernadou

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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