دانلود رایگان مقاله راه حل تحلیلی برای پرتوها با شرایط مرزی در پایه الاستیک دو پارامتری

ABSTRACT

An efficient analytical method is presented for the closed form solution of continuous beams on two-parameter elastic foundations. The general form of the governing equation is reduced to a system of first-order differential equations with constant coefficients. The system is then solved using Jordan form decomposition for the coefficient matrix and construction of the fundamental solution. Common types of boundary conditions (pinned and roller support, hinge connection, fixed and free end) can be applied to an arbitrary point on the beam. The method has a completely computer-oriented algorithm, computational stability, and optimal conditionality of the resultant system and is a powerful alternative to the analytical solution of beams with multipoint boundary conditions on one- or twoparameter elastic foundations. Examples with different types of loading, boundary conditions, and foundation are presented to verify the method.

7. Conclusion

The examples given demonstrate the advantages of the proposed approach for an analytical solution to a continuous beam on one or two-parameter elastic foundations. The method has a completely computer-oriented algorithm, computational stability, optimal conditionality of the resultant system, and is applicable for different loads at an arbitrary point or region on the beam. In addition, common boundary conditions such as pinned and roller supports, hinge connections, and fixed and free ends at arbitrary points along the beam, can be considered. Structural or foundation discontinuities (changes in the physical properties of the beam or foundation) can be applied by changing the coefficient matrix at the relevant interval. The method has been shown to be a powerful alternative to the analytical solution of beams with multipoint boundary conditions on one or two-parameter elastic foundations, especially for programming of specialized software packages oriented to analytical solutions. In future research, the analytical solution for curved beams on elastic foundations and beams on infinite elastic foundations with additional internal boundary points can be investigated.