Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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EQUATIONS OF MOTION FOR CRACKED BEAMS AND SHALLOW ARCHES

  • Gutman, Semion (Department of Mathematics, University of Oklahoma) ;
  • Ha, Junhong (School of Liberal Arts, Korea University of Technology and Education) ;
  • Shon, Sudeok (Department of Architectural Engineering, Korea University of Technology and Education)
  • Received : 2021.12.01
  • Accepted : 2022.01.17
  • Published : 2022.06.08
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Abstract

Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the first principles using the Extended Hamilton's Principle, accounting for non-conservative forces. The variational formulation of the equations is stated in terms of the subdifferentials of the bending and axial potential energies. The equations are given in their abstract (weak), as well as in classical forms.

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Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1I1A1A01065032). And this paper was supported by Education and Research promotion program of the KOREATECH in 2021.

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