TY - THES A1 - Ren, Huilong T1 - Dual-horizon peridynamics and Nonlocal operator method N2 - In the last two decades, Peridynamics (PD) attracts much attention in the field of fracture mechanics. One key feature of PD is the nonlocality, which is quite different from the ideas in conventional methods such as FEM and meshless method. However, conventional PD suffers from problems such as constant horizon, explicit algorithm, hourglass mode. In this thesis, by examining the nonlocality with scrutiny, we proposed several new concepts such as dual-horizon (DH) in PD, dual-support (DS) in smoothed particle hydrodynamics (SPH), nonlocal operators and operator energy functional. The conventional PD (SPH) is incorporated in the DH-PD (DS-SPH), which can adopt an inhomogeneous discretization and inhomogeneous support domains. The DH-PD (DS-SPH) can be viewed as some fundamental improvement on the conventional PD (SPH). Dual formulation of PD and SPH allows h-adaptivity while satisfying the conservations of linear momentum, angular momentum and energy. By developing the concept of nonlocality further, we introduced the nonlocal operator method as a generalization of DH-PD. Combined with energy functional of various physical models, the nonlocal forms based on dual-support concept are derived. In addition, the variation of the energy functional allows implicit formulation of the nonlocal theory. At last, we developed the higher order nonlocal operator method which is capable of solving higher order partial differential equations on arbitrary domain in higher dimensional space. Since the concepts are developed gradually, we described our findings chronologically. In chapter 2, we developed a DH-PD formulation that includes varying horizon sizes and solves the "ghost force" issue. The concept of dual-horizon considers the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly with arbitrary particle discretization. All three peridynamic formulations, namely bond based, ordinary state based and non-ordinary state based peridynamics can be implemented within the DH-PD framework. A simple adaptive refinement procedure (h-adaptivity) is proposed reducing the computational cost. Both two- and three- dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. In chapter 3, a nonlocal operator method (NOM) based on the variational principle is proposed for the solution of waveguide problem in computational electromagnetic field. Common differential operators as well as the variational forms are defined within the context of nonlocal operators. The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease, which is necessary for the eigenvalue analysis of the waveguide problem. The present formulation is applied to solve 1D Schrodinger equation, 2D electrostatic problem and the differential electromagnetic vector wave equations based on electric fields. In chapter 4, a general nonlocal operator method is proposed which is applicable for solving partial differential equations (PDEs) of mechanical problems. The nonlocal operator can be regarded as the integral form, ``equivalent'' to the differential form in the sense of a nonlocal interaction model. The variation of a nonlocal operator plays an equivalent role as the derivatives of the shape functions in the meshless methods or those of the finite element method. Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease. The nonlocal operator method is enhanced here also with an operator energy functional to satisfy the linear consistency of the field. A highlight of the present method is the functional derived based on the nonlocal operator can convert the construction of residual and stiffness matrix into a series of matrix multiplications using the predefined nonlocal operators. The nonlocal strong forms of different functionals can be obtained easily via the concept of support and dual-support. Several numerical examples of different types of PDEs are presented. In chapter 5, we extended the NOM to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original NOM in chapter 3 and chapter 4, which can only achieve one-order convergence. The higher order NOM obtains all partial derivatives with specified maximal order simultaneously without resorting to shape functions. The functional based on the nonlocal operators converts the construction of residual and stiffness matrix into a series of matrix multiplication on the nonlocal operator matrix. Several numerical examples solved by strong form or weak form are presented to show the capabilities of this method. In chapter 6, the NOM proposed as a particle-based method in chapter 3,4,5, has difficulty in imposing accurately the boundary conditions of various orders. In this paper, we converted the particle-based NOM into a scheme with interpolation property. The new scheme describes partial derivatives of various orders at a point by the nodes in the support and takes advantage of the background mesh for numerical integration. The boundary conditions are enforced via the modified variational principle. The particle-based NOM can be viewed a special case of NOM with interpolation property when nodal integration is used. The scheme based on numerical integration greatly improves the stability of the method, as a consequence, the operator energy functional in particle-based NOM is not required. We demonstrated the capabilities of current method by solving the gradient solid problems and comparing the numerical results with the available exact solutions. In chapter 7, we derived the DS-SPH in solid within the framework of variational principle. The tangent stiffness matrix of SPH can be obtained with ease, and can be served as the basis for the present implicit SPH. We proposed an hourglass energy functional, which allows the direct derivation of hourglass force and hourglass tangent stiffness matrix. The dual-support is {involved} in all derivations based on variational principles and is automatically satisfied in the assembling of stiffness matrix. The implementation of stiffness matrix comprises with two steps, the nodal assembly based on deformation gradient and global assembly on all nodes. Several numerical examples are presented to validate the method. KW - Peridynamik KW - Variational principle KW - weighted residual method KW - gradient elasticity KW - phase field fracture method KW - smoothed particle hydrodynamics KW - numerical methods KW - PDEs Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210412-44039 ER - TY - THES A1 - Büchner, Stefan T1 - Methoden zur Ermittlung von Materialkennwerten für numerische Berechnungen in der Geotechnik T1 - Methods for investigation of soil properties for numerical calculations in geotechnics N2 - Bei der Bearbeitung geotechnischer Aufgabenstellungen treten häufig Probleme bei der Vorhersage des Setzungsverhaltens von Böden auf. Numerische Methoden auf Basis finiter Elemente oder finiter Differenzen werden oftmals als Hauptinstrumente der Prognose verwendet. Dabei erzielen sie jedoch nicht selten Ergebnisse, die im Nachhinein als unbefriedigend bezeichnet werden müssen. Eine Begründung dafür liegt in der Verwendung linearer Stoffgesetze, die auf Ansätze aus der Elastizitätstheorie beruhen. Werden höherwertige Stoffgesetze eingesetzt, so fehlen oftmals gesicherte Aussagen zu den erforderlichen Bodenkennwerten. Diese müssen durch ein umfangreiches Versuchsprogramm mit einer aufwendigen Auswertung bestimmt werden. Ziel dieser Arbeit ist es daher, eine robuste Methode zu entwickeln, die in der Lage ist, aus Messwerten (Feld) und Versuchsergebnissen (Labor) geeignete Parameter für Modelle mit nichtlinearer Konsolidationstheorie zu ermitteln. Dazu werden die Möglichkeiten der Mathematik ausgenutzt, welche inverse Methoden zur Verfügung stellt, mit denen man mehrere Bodenkennwerte (hauptsächlich Steifigkeiten und Durchlässigkeiten) gleichzeitig unter Be-rücksichtung ihrer Wechselbeziehungen zueinander bestimmen kann. Als Instrumentarium dafür steht das Programm AdConsol-1D zur Verfügung, welches die inverse Parameterermittlung auf Basis mathematischer Optimierungsmethode ermöglicht. Ein Test- und Versuchsdamm, der im Finnischen Haarajoki (Haarajoki Test Embankment) errichtet wurde und über längeren Zeitraum messtechnisch überwacht wurde, dient als Validationsbeispiel. Dieser wurde auf sehr verformungsempfindlichem Boden errichtet. Durch Aufbereitung und Auswertung der Feld- und Laborversuche am Haarajoki Test Embankment wurden die Grundlagen für die inverse Parameterermittlung geschaffen. Dazu wurde eine Methode zur Konstruktion plausib-ler Porenwasserüberdrücke aus Setzungsmessungen und Laborversuchsdaten entwickelt. Mit den Werten der Optimierung wurde ein Modell im 2D FEM Programm Plaxis erstellt, welches die in Haarajoki gemessenen Setzungen und Porenwasserdrücke möglichst genau reproduzieren sollte. Es zeigte sich, dass sich Bodenparameter des eindimensionalen nichtlinearen Konsolidati-onsmodells nicht problemlos auf ein 2D FEM Modell übertragen lassen. Insbesondere fehlen gesicherte Aussagen über die Größe des horizontalen Durchlässigkeitskoeffizienten kx und des Referenzsekantenmoduls E50Ref aus dem Triaxialversuch. Die inverse Berechnung für sich betrachtet verlief dahingegen zufrieden stellend mit dem eindimensionalen Modell in AdConsol-1D. Auf dieser Grundlage ist die Erstellung einer realistischen Prognose des weiteren Konsolidationsverlaufes am Haarajoki Test Embankment möglich. N2 - In geotechnics, problems frequently appear in the prediction of settlements for soils. Numerical Methods based on Finite Elements or Finite Differences are often used as main instruments for prediction. These methods often produce unsatisfying results. One reason is the utilization of linear material laws which are based on the theory of elasticity. Introducing ad-vanced material laws secure informations lack for required soil parameters. They need to be determined in an extensive test programm with complex evaluation.The intention is, to develop a robust method, which is able to determine adequate parameters from measurements and laboratory examinations using a one dimensional nonlinear theory of consolidation. In addidtion the possibilities of mathematics are used, which provide invers methods for the simultaneous determination of several soil parameters (especially stiffness and permeability parameters) and their correlations. As instrument the programm AdConsol-1D was available, which offers the invers parameter investigation on basis of mathematical optimization meth-ods. An embankment for tests and examination, the Haarajoki Test Embankment serves as validation example. Pore pressures and cumulative settlements were observed for a long time period at the embankment, which was built on very soft soil. The conditioning and evaluation of field and laboratory tests from the Haarajoki Test Embankment accomplished a basis for the invers parameter determination. For that purpose a method for designing plausible excess pore pressures, using measurements of settlements and laboratory test datas, was developed. A model was constracted with the 2D FEM programm Plaxis using the values from the opti-mization, which ought to reproduce the measured settlements and excess pore pressures from Haarajoki Test Embankment as accurately as possible. It was shown, that the soil properties from the one-dimensional non-linear consolidation model can’t be assigned without problems onto a 2D FEM model. Especially lack firmed information about the value of horizontal permeability kx and the modulus for the secant stiffness in standard drained triaxial tests (E50Ref). Whereas the invers calculation itself produced a satisfying result with the one-dimensional model of AdConsol-1D. On that basis the construction of a realistic prediction of former consolidation process at Haarajoki Test Embankment is possible. KW - Konsolidation KW - Inverses Problem KW - Bodenmechanik KW - Parameterschätzung KW - Kennwertermittlung KW - nichtlineare Konsolidationstheorie KW - numerische Berechnungen KW - mathematische Optimierungsmethoden KW - non-linear consolidation KW - determination of soil properties KW - numerical methods Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-5524 N1 - Der Volltext-Zugang wurde im Zusammenhang mit der Klärung urheberrechtlicher Fragen mit sofortiger Wirkung gesperrt. ER -