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مجله بین المللی مکانیک غیر خطی
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  • on a pure complementary energy principle and a force-based finite element formulation for non-linear elastic cables

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    • تاریخ ارائه: 1392/07/24
    • تاریخ انتشار در تی پی بین: 1392/07/24
    • تعداد بازدید: 885
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     a complementary-dual force-based finite element formulation is proposed for the geometrically exact quasi-static analysis of one-dimensional hyperelastic perfectly flexible cables lying in the two-dimensional space. this formulation employs as approximate functions the exact statically admissible force fields, i.e., those that satisfy the equilibrium differential equations in strong form, as well as the equilibrium boundary conditions. the formulation relies on a principle of total complementary energy only expressed in terms of force fields, being therefore called a pure principle. under the assumption of stress-unilateral behavior, this principle can be regarded as being dual to the principle of minimum total potential energy, corresponding therefore to a maximum principle. some numerical applications, including cables suspended from two and three points at the same level or at different levels, with both hookean and neo-hookean material behaviors, are presented. as it will be shown, in contrast to the standard two-node displacement-based formulation derived from the principle of minimum total potential energy, the proposed dual force-based formulation is capable of providing the exact solution of a given problem only using a single finite element per cable. both the proposed principle of pure complementary energy and its corresponding force-based finite element formulation can be easily extended to the case of cables lying in the three-dimensional space.

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