دانلود رایگان مقاله حذف self-straining در فرمولاسیون شعاع منحنی تیموشنکو در مختصات منحنی الخط

Abstract

Isogeometric formulations of curved Timoshenko beams in curvilinear coordinates often result in self-straining of membrane and shear strains, due to the discretization of the local displacement field. Self-straining means a failure in exact representation of rigid body motions, which consequently deteriorates response quality. To overcome the difficulty of self-straining, we propose an invariant formulation that discretizes the global displacement field. It turns out that the approximated membrane, shear, and bending strain measures are invariant regardless of initial geometry in the proposed formulation. For effective applications to any arbitrarily curved structures and locking-free formulations to alleviate membrane and shear locking, the proposed invariant formulation is combined with selective reduced integration (SRI) and B¯ projection method. Numerical examples demonstrate the effectiveness and applicability of the proposed invariant formulation, which gives much more accurate results together with both SRI and B¯ projection method, in comparison to the existing isogeometric formulations.

5. Conclusions

In this paper, we observe self-straining phenomena in existing isogeometric formulations of curved Timoshenko beams. Self-straining gets worse as the curvature variation of domain increases and has significant influence on the accuracy of response analysis. Self-straining can be reduced more or less through h-refinement as the initial curvature variation of elements decreases, however, it is apparent that the persisting oscillations in the refined model significantly deteriorate the response quality. In the existing formulation, a numerical example demonstrates that the membrane and shear strain energy constitutes a half of total strain energy, which is mainly due to the spurious membrane and shear strains generated by self-straining that appears as a serious spurious constraint in the curved region. In the proposed invariant formulation that uses the discretization of the global displacement field, it is shown that self-straining can be completely eliminated. Through various numerical examples, we verify the significance of the proposed invariant formulation to achieve accurate results for arbitrarily curved beams.