Enhanced integration methods for the peridynamic theory.

dc.contributor.authorYu, Kebing
dc.date.accessioned2011-07-28T15:03:58Z
dc.date.available2011-07-28T15:03:58Z
dc.date.graduationmonthAugust
dc.date.issued2011-07-28
dc.date.published2011
dc.description.abstractPeridynamics 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.
dc.description.advisorKevin B. Lease
dc.description.advisorXiao J. Xin
dc.description.degreeDoctor of Philosophy
dc.description.departmentDepartment of Mechanical and Nuclear Engineering
dc.description.levelDoctoral
dc.identifier.urihttp://hdl.handle.net/2097/10750
dc.language.isoen_US
dc.publisherKansas State University
dc.rights© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectPeridynamics
dc.subjectIntegration
dc.subjectAdaptive
dc.subjectGaussian
dc.subject.umiMechanical Engineering (0548)
dc.titleEnhanced integration methods for the peridynamic theory.
dc.typeDissertation

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