Graduate and Postdoctoral Studies
Peridynamics and Applications
Friday, April 14, 2017
to 5:00 PM
128 Mechanical Engineering Building
Peridynamics as a nonlocal elasticity theory shows advantages when solving problems involve crack. Unlike classical continuum mechanics, Peridynamics involves integral term to represent material responses. In this thesis, dynamic responses of Peridynamics finite bar with specified boundary condition will be proposed. Results show consistencies of Peridynamics with classical elasticity theory. Peridynamics solution is erratic at boundary region due to the fact that stiffness is changed on boundary. Inspired by the fact that Peridynamics reduced to continuum mechanics when horizon goes to zero, Varying Horizon Approach is introduced to represent Peridynamic responses at boundary region.
Nonlocal beam bending equation is proposed based on peridynamics. This proposed nonlocal bending equation reduces to Euler Bernoulli bending equation when nonlocal parameter goes to zero. Analytical and numberical responses of derived nonlocal bending equation with different nonlocal parameters are analyzed and compared with responses of Euler Bernoulli beam. Peridynamic beam equation has advantages over Euler Bernoulli beam equation when solving beam responses with initial crack or beam with discontinuous cross sections. Navier Stokes equation is also reformulated based on Peridynamic concepts. Advection and diffusion terms in Navier Stokes equation are reformulated nonlocally. This thesis will show that reformulated nonlocal Navier Stokes equation follows equilibrium of momentum. Numerical examples of both Navier Stokes equation and nonlocal Navier Stokes equation are provided.
In the final application, an efficient algorithm to model rock crack process based on peridynamics will be developed. This model iterates adaptively with the propagation of crack and with the penetration of drill bit. Relationship of Penetration rate with weight on bit, rotary speed, axial vibration frequency and amplitude will also be investigated.