Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Kevin B. Lease / Xiao J. Xin / Peridynamics is a non-local continuum theory that formulates problems in terms of
integration of interactions between the material points. Because the governing equation
of motion in the peridynamic theory involves only integrals of displacements, rather than
derivatives of displacements, this new theory offers great advantages in dealing with problems
that contain discontinuities. Integration of the interaction force plays an important
role in the formulation and numerical implementation of the peridynamic theory. In this
study two enhanced methods of integration for peridynamics have been developed. In the
first method, the continuum is discretized into cubic cells, and different geometric configurations
over the cell and the horizon of interaction are categorized in detail. Integration
of the peridynamic force over different intersection volumes are calculated accurately using
an adaptive trapezoidal integration scheme with a combined relative-absolute error control.
Numerical test examples are provided to demonstrate the accuracy of this new adaptive
integration method. The bond-based peridynamic constitutive model is used in the calculation
but this new method is also applicable to state-based peridynamics. In the second
method, an integration method with fixed Gaussian points is employed to accurately calculate
the integration of the peridynamic force. The moving least square approximation
method is incorporated for interpolating the displacement field from the Gaussian points.
A compensation factor is introduced to correct the soft boundary effect on the nodes near
the boundaries. This work also uses linear viscous damping to minimize the dynamic effect
in the solution process. Numerical results show the accuracy and effectiveness of this
Gaussian integration method. Finally current research progress and prospective directions
for several topics are discussed.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/10750 |
| Date | January 1900 |
| Creators | Yu, Kebing |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
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