04926nam 2200457 450 991062726450332120230225111413.03-031-06340-6(CKB)5850000000078588(MiAaPQ)EBC7101991(Au-PeEL)EBL7101991(PPN)264959108(EXLCZ)99585000000007858820230225d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA new Kirchhoff-Love beam element and its application to polymer mechanics /Matthias C. SchulzCham, Switzerland :Springer International Publishing,[2022]©20221 online resource (150 pages)Mechanics and Adaptronics Ser.3-031-06339-2 Intro -- Preface -- Zusammenfassung -- Summary -- Contents -- List of Figures -- List of Tables -- 1 Introduction -- 1.1 Motivation -- 1.2 Focus of This Thesis -- 1.3 Relevance of the Present Work -- 1.4 Outline -- 2 Modeling of Slender Bodies -- 2.1 A General Model for Physical Space -- 2.2 Definition of Slender Bodies -- 2.3 The Special Orthogonal Group SO(3) -- 2.3.1 The Tangent Space of SO(3) and the Corresponding Exponential Map -- 2.3.2 Derivatives and Variations of Orthogonal Transformations -- 2.3.3 Parameterization of Orthogonal Rotations -- 2.4 Simo-Reissner Beam Formulation -- 2.4.1 Kinematic Assumptions and Description -- 2.4.2 Balance of Linear and Angular Momentum -- 2.4.3 Weak Form and Resulting Deformation Measures -- 2.4.4 Constitutive Relations -- 2.5 Kirchhoff-Love Beam Formulations -- 2.5.1 Advantages of Kirchhoff-Love Beam Formulations -- 2.5.2 Kirchhoff-Love Beam Formulation Based on Constraint Translation -- 2.5.3 Kirchhoff-Love Beam Formulation Based on Constraint Rotation -- 2.5.4 Kirchhoff-Love Beam Formulations Based on Weak Enforcement -- 2.5.5 Reduced Kirchhoff-Love Beam Formulations -- 2.5.6 Analytical Formulation of Kirchhoff-Love Beams -- 3 Finite-Element Formulation of Slender Bodies Modeled by Geometrically Exact Beams -- 3.1 Discretization in Time -- 3.1.1 Identification of Primary Fields -- 3.1.2 Generalized-alphaα Method for Elements of double struck upper RmathbbR and double struck upper R cubedmathbbR3 -- 3.1.3 Generalized-alphaα Method for Elements of bold upper S upper O bold left parenthesis bold 3 bold right parenthesisSO(3) -- 3.1.4 Order of Temporal and Spatial Discretization -- 3.2 Discretization in Space -- 3.2.1 Essentials of the Finite-Element Method -- 3.2.2 Discretization of Elements of double struck upper RmathbbR and double struck upper R cubedmathbbR3.3.2.3 Discretization of Elements of upper S upper O left parenthesis 3 right parenthesisSO(3) -- 3.3 Simo-Reissner Beam Element -- 3.4 Kirchhoff-Love Beam Elements -- 3.4.1 Kirchhoff-Love Beam Elements Based on Constraint Translation -- 3.4.2 Inextensible Kirchhoff-Love Beam Element -- 3.4.3 Kirchhoff-Love Beam Elements Based on Weak Enforcement -- 3.4.4 Nested Assembly Processes -- 3.4.5 Dirichlet Boundary Conditions and Joints -- 3.5 Requirements of Beam Formulations -- 3.5.1 Differentiability of Spatially Discretized Fields -- 3.5.2 Objectivity and Path-Independence -- 3.5.3 Numerical Locking -- 3.5.4 Conservation Properties -- 3.5.5 Optimal Convergence Order -- 3.6 Numerical Examples -- 3.6.1 Objectivity -- 3.6.2 Path-Independence -- 3.6.3 Locking and Convergence Order -- 3.6.4 Performance -- 3.6.5 Free Oscillation -- 4 Modeling the Mechanics of Single Polymer Chains in the Finite-Element Framework -- 4.1 Basic Model Assumptions -- 4.2 Probabilistic Basics -- 4.3 Viscous and Temperature Effects -- 4.3.1 Viscous Forces and Moments -- 4.3.2 Stochastic Forces and Moments -- 4.4 Constitutive Parameters and Discretization -- 4.5 Surrogate Modeling -- 4.5.1 Linear Model for Regression -- 4.5.2 Gaussian Process Regression -- 4.6 Numerical Results -- 4.6.1 Distributions for Different Boundary Conditions and Loads -- 4.6.2 Tracking the Accuracy of Monte Carlo Methods -- 4.6.3 Obtaining Force-Extension Curves -- 4.6.4 Surrogate Modeling and Validation -- 4.6.5 Fit to Experimental Data in a Bayesian Framework -- 5 Conclusion -- 5.1 Novel Geometrically Exact Kirchhoff-Love Beams -- 5.2 Finite-Element Brownian Dynamics Simulations for Bayesian Inference -- Bibliography.Mechanics and Adaptronics Ser.PolymersMechanical propertiesFinite element methodPolymersMechanical properties.Finite element method.620.192Schulz Matthias C.1267650MiAaPQMiAaPQMiAaPQBOOK9910627264503321A New Kirchhoff-Love Beam Element and Its Application to Polymer Mechanics2981757UNINA