Stability of the Size-Dependent and Functionally Graded Curvilinear Timoshenko Beams; Journal of Computational and Nonlinear Dynamics; Vol. 12, iss. 4
| Parent link: | Journal of Computational and Nonlinear Dynamics Vol. 12, iss. 4.— 2017.— [041018, 8 p.] |
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| সংস্থা লেখক: | |
| অন্যান্য লেখক: | , , , , |
| সংক্ষিপ্ত: | Title screen The size-dependent model is studied based on the modified couple stress theory for the geometrically nonlinear curvilinear Timoshenko beam made from a functionally graded material having its properties changed along the beam thickness. The influence of the size-dependent coefficient and the material grading on the stability of the curvilinear beams is investigated with the use of the setup method. The second-order accuracy finite difference method is used to solve the problem of nonlinear partial differential equations (PDEs) by reducing it to the Cauchy problem. The obtained set of nonlinear ordinary differential equations (ODEs) is then solved by the fourth-order Runge–Kutta method. The relaxation method is employed to solve numerous static problems based on the dynamic approach. Eight different combinations of size-dependent coefficients and the functionally graded material coefficient are used to study the stress-strain responses of Timoshenko beams. Stability loss of the curvilinear Timoshenko beams is investigated using the Lyapunov criterion based on the estimation of the Lyapunov exponents. Beams with/without the size-dependent behavior, homogeneous beams, and functionally graded beams having the same stiffness are investigated. It is shown that in straight-line beams, the size-dependent effect decreases the beam deflection. The same is observed if the most rigid layer is located on the top of the beam. In the curvilinear Timoshenko beam, such a location of the most rigid layer essentially improves the beam strength against stability loss. The observed transition of the largest Lyapunov exponent from a negative to positive value corresponds to the transition from a precritical to postcritical beam state. |
| ভাষা: | ইংরেজি |
| প্রকাশিত: |
2017
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | http://dx.doi.org/10.1115/1.4035668 |
| বিন্যাস: | বৈদ্যুতিক গ্রন্থের অধ্যায় |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=653768 |
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| 200 | 1 | |a Stability of the Size-Dependent and Functionally Graded Curvilinear Timoshenko Beams |f J. Awrejcewicz [et al.] | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 330 | |a The size-dependent model is studied based on the modified couple stress theory for the geometrically nonlinear curvilinear Timoshenko beam made from a functionally graded material having its properties changed along the beam thickness. The influence of the size-dependent coefficient and the material grading on the stability of the curvilinear beams is investigated with the use of the setup method. The second-order accuracy finite difference method is used to solve the problem of nonlinear partial differential equations (PDEs) by reducing it to the Cauchy problem. The obtained set of nonlinear ordinary differential equations (ODEs) is then solved by the fourth-order Runge–Kutta method. The relaxation method is employed to solve numerous static problems based on the dynamic approach. Eight different combinations of size-dependent coefficients and the functionally graded material coefficient are used to study the stress-strain responses of Timoshenko beams. Stability loss of the curvilinear Timoshenko beams is investigated using the Lyapunov criterion based on the estimation of the Lyapunov exponents. Beams with/without the size-dependent behavior, homogeneous beams, and functionally graded beams having the same stiffness are investigated. It is shown that in straight-line beams, the size-dependent effect decreases the beam deflection. The same is observed if the most rigid layer is located on the top of the beam. In the curvilinear Timoshenko beam, such a location of the most rigid layer essentially improves the beam strength against stability loss. The observed transition of the largest Lyapunov exponent from a negative to positive value corresponds to the transition from a precritical to postcritical beam state. | ||
| 461 | |t Journal of Computational and Nonlinear Dynamics | ||
| 463 | |t Vol. 12, iss. 4 |v [041018, 8 p.] |d 2017 | ||
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