PROF. HOLM ALTENBACH
On the Application of Peridynamic Framework to First-order Shear Deformation Beam Theory
Holm Altenbach1,2, Konstantin Naumenko2, and Zhenghao Yang2
1Ton Duc Thang University, 2Otto-von-Guericke-Universität Magdeburg
Abstract:
Nonlocal continuum theories have gained increasing attention for modeling classical and advanced materials. Peridynamics offers a robust nonlocal framework by incorporating long-range mechanical interactions between material points. However, an internal length scale parameter called horizon should be established.
The present study discusses an analytical study of peridynamic first-order shear deformation (FSDT) beam equations under both static and dynamic loading conditions, considering various boundary constraints. In comparison with the classical beam theories allowing numerous closed-form solutions, analytical results for peridynamic formulations remain rarely. For static cases, the derived bending moment and shear flux solutions coincide with classical FSDT stress resultants. For dynamic problems, solutions for free vibrations, forced vibrations, and lateral impact of simply supported beams are presented, showing excellent agreement with classical FSDT solutions when the horizon is sufficiently small.