Enhanced integration methods for the peridynamic theory.

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dc.contributor.author Yu, Kebing
dc.date.accessioned 2011-07-28T15:03:58Z
dc.date.available 2011-07-28T15:03:58Z
dc.date.issued 2011-07-28
dc.identifier.uri http://hdl.handle.net/2097/10750
dc.description.abstract 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. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Peridynamics en_US
dc.subject Integration en_US
dc.subject Adaptive en_US
dc.subject Gaussian en_US
dc.title Enhanced integration methods for the peridynamic theory. en_US
dc.type Dissertation en_US
dc.description.degree Doctor of Philosophy en_US
dc.description.level Doctoral en_US
dc.description.department Department of Mechanical and Nuclear Engineering en_US
dc.description.advisor Kevin B. Lease en_US
dc.description.advisor Xiao J. Xin en_US
dc.subject.umi Mechanical Engineering (0548) en_US
dc.date.published 2011 en_US
dc.date.graduationmonth August en_US

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