Domain-boundary element method for elastodynamics of functionally graded Timoshenko beams. (15th January 2018)

• Record Type: Journal Article
• Authors: Eshraghi, Iman; Dag, Serkan
• Is Part Of: Computers & structures. Volume 195(2018)
• Page Start: 113
• Page End: 125
• Publication Date: 2018-01-15
• Subjects: Domain-boundary element method -- Elastodynamics -- Forced vibrations -- Functionally graded materials -- Timoshenko beam; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2017.10.007
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: A domain-boundary element method is developed for elastodynamics of graded beams. Differential equations are derived considering variations of physical properties. Static fundamental solutions are used in weighted residual statements. Integral equations are reduced to time-dependent ordinary differential equations. Parametric analyses are carried out for graded beams under various loadings. Abstract: A new domain-boundary element method is developed for elastodynamic analysis of functionally graded Timoshenko beams. Three governing partial differential equations of motion are derived by considering through-the-thickness variations of the physical properties. Weighted-residual forms are imposed utilizing the static fundamental solutions. These forms are then reduced to three integral equations containing domain integrals with time derivatives of unknown functions. Through domain discretization and shape function approximation, integral equations are converted to a system of ordinary differential equations in time. Forced dynamic response is revealed by solving the system of equations via Houbolt method. Comparison of dynamic responses generated for homogeneous beams to those calculated through an analytical solution and finite difference method verify the developed procedures. Further parametric analyses are performed for functionally graded Timoshenko beams under step, harmonic, and impulsive loadings. The numerical results presented illustrate the influence of material inhomogeneity on time histories of deflection and stress. Domain-boundary element method is demonstrated to be an effective technique for elastodynamic analysis of functionally graded structures.