Enhanced geometrically-nonlinear poro-FG shear-deformable beams under moving load in discrete state-space

ABSTRACT

Using Hamilton’s principle, the motion-governing partial differential equations of enhanced geometrically-nonlinear porous functionally-graded beam subjected to a concentrated moving force were derived and compare d with the corresponding geometrically-nonlinear beam. The beam density and elastic modulus vary continuously along the web direction from those of metal to those of ceramic. The motion-governing difference equations were achieved via generalized differential quadrature and the Newmark’s methods, assembled via state-spatial variables and their velocities, and solved via Newton-Raphson stabilized iterations. Components of the beam dynamic elastica, shearing force and flexural moment were obtained along the span. Proportionality of nonporous-FG beam deflection, to porosity, to material parameter, and to metal portion vis-à-vis ceramic, and that of poro-FG beamanti-symmetry in deflection, to load speed was revealed. The critical speed of the load that causes the locally-greatest displacements was found. Cross-sectional shearing and normal stresses were obtained at mid-span, across the web. As a particular case, the beam motion-governing difference equations were reduced to equilibrium-governing ones and solved. The lateral displacement of the beam static elastica was compared with that of the corresponding nonlinear and linear beams.

KEYWORDS:

• Moving load
• poro-FG geometrically-nonlinear beam
• dynamic elastica
• gdq and newmark’s discretizations
• positional and time state-spatial variables
• critical load speed
• extra elastic and kinetic terms

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors confirm that the research was not funded by any organizations.

Notes on contributors

Peyman Azartash

Mr. Peyman Azartash was graduated with master of science degree in mechanical engineering from the department of mechanical engineering of the Islamic Azad University-South Tehran Branch in Tehran, Iran

S. Mahdi Khorsandijou

Dr. S. Mahdi Khorsandijou is assistant professor in the Islamic Azad University-South Tehran Branch in Tehran, Iran

Ahmad Reza Khorshidvand

Dr. Ahmad Reza Khorshidvand is associate professor in the Islamic Azad University-South Tehran Branch in Tehran, Iran