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Michell structures / Tomasz Lewiński, Tomasz Sokół, Cezary Graczykowski. - Cham : Springer International Publishing AG, 2019. - XVII, [1], 569 stron : ilustracje, wykresy ; 25 cm.

Autor

Lewiński Tomasz. Sokół Tomasz. Graczykowski Cezary.

Forma i typ

Książki Publikacje naukowe

Temat

Michell, Anthony George Maldon (1870-1959). Mechanika konstrukcji

Dziedzina i ujęcie

Inżynieria i technika

Bibliografia przy rozdziale.

Equilibrium Problems of Elastic Frames, Thin Plates in Bending and Membrane Shells A Single Straight and Prismatic Bar Plane Frames Made of Compressible Bars Plane Frames of Incompressible Bars Grillages of Rigid Joints . Systems of Beams The Spatial Frames Trusses I.2.8 The Variational Continuum Approach to Statics of Plane Frames, Systems of Beams and Trusses: The Theorems on Minimum of the Elastic Potential and of the Minimum Complementary Energy. The Spatial Frames. The Descretized Versions of the Theorems on the Minimum of the Elastic Potential and of the Minimum of Complementary Energy. Thin Plates in Bending Membrane Shells Optimum Design of Sbuctures of Finite Number of Bars. Single Load Vańant Trusses of Minimal Compliance and Fixed Volume The lrast Volume Trusses of Bounded Stress kvel Maxwell'sTheorem on Geometric Properties of the Least Volume Symmetric Cantilever Trussęs of Prescribed Number of Nodes The least Compliant Beams and Systems of Beams The Continuum Formulation of the Optimum Design Problem Construction of the Optimum Solution and Its Properties The Algebraic Approach. Examples of optimal Beams Least Compliant Systems of Beams. A Simplified Approach for Dense Layouts of Bars. The Stiffest Grillages of rigid Joints . Standard Approach Case of Negligible Torsional Stiffness A Simplified Approach for Dense Grillages Theory of Michell Structures. Single Load Case Kinematic Formulation. Case of Equal Permissible Stresses Orthogonal Curvilinear Parameterization In Tensionand Compression Static Formulation. Reconstruction of the Optimal Continuum Body of Irast Compliance Corresponding to Michell's Problem Kinematic Formulation for the ŻD and 3D Settings. Static Formulation Geometric and Kinematic Description Equilibrium Equations in Lines of Trajectories of Principal Stresses Hencky and Michell Nets Composed of Two Families of Curves. Kinematic Consideration Geometric Properties of Hencky Nets Construction of the Displacement Fields within Hencky's Parameterization. Michell's Nets The Riemann Method of Solving the Problems Governed by the Equation 4.3 Statics of a Continuum Body Parameterized by Curvilinear Michell Nets A Body Without Reinforcing Ribs The euilibrium of a Fibrous Structure Reinforced by Ribs Parameterization of the Subdomains in the Regimes JR1, JR2: The Nets Including Families of Staight Lines. Kinematics And equilibrium Conditions The Nets Including One Family of Straight Lines The Michell Nets Parameterized by the Polar Coordinate System The Simplest Michell Structures The Two-Force Problem in the Plane The Lightest Cantilever Transmitting a Point Load to a Straight Support The Simplest Three-Force Problem: Case of Three Parallel Forces Hemp's Problem of Transmitting a Vertical Force to Two Fixed Supports. The Full-Plane Design Symmetric Problem of Three Parallel Forces in the Plane The problem of the Exterior of a Circle The Hencky Net Composed of Logarithmic Spirals Non_existence of Displacement Fields (z' v) Associated with the Hencky Net for rc I I The Optimal Wheel A Family of Suboptimal Solutions-Illustrative Examples of Trusses of Finite Number of Bars The Problem of the Interior of a Circle The Optimal Wheel The Point Load Within the Domain Transmitting a Point load to a Segment of a Straight Support' Full Plane Designs Formulation of the Problem and the Simplest Forms of the Solutions The Cantilevers Supported on Two Circles Cantilevers with a Three-Sided Polygonal Support. Construction of the Michell Net and the Adjoint Displacement Fields. Symmetric Case The Case of Asymmetry Cantilevers Supported on a Square The Michell Net The Adjoint Displacement Fields Geometry of the Michell Net Optimal Structures for Selected Positions of the Point Load . . Towards Finding Michell Nets in the Bounded Domains: Additional Mathematical Tools Selected Laplace Transforms of Chan's Functions Riomannns Formula: An Alternative Version Cantilevers Constructed Within Trapezoidal Domains. Geometry of Michell's Nets Including H'S.Y. Chan's Domains Adoint Displacement Fields Force Fields Density of Fibreś and Computation of the Volumes of Michell's Cantilevers Deep Beam Problem Solution of the Auxiliary Problem Optimal Designs of Deep Beams Subjected to Point Loads at the Upper Edge shaped Domains Solution of the Auxiliary Problem The Solution to the Initial hoblem (the Elbow Problem) Illustrative Examples Case of an Inclined lłwer Boundary and the Vertical Point Load Cases of Non-vertical Point Load The Three-Force Problem. Subclasses of a General Solution Three-Force Problem in the Whole Plane Simply Supported Michell Trusses Generated by a Point Load. Half-Plane Solutions Optimal Pin-supported Girders Subjected to Symmetrically Located Vertical Forces Case of Two Forces. Half-Plane Solutions Case of Three, Seven and 199 Forces. Half-Plane Solutions Full-Plane Solutions Optimal Layouts Constained by the Allowable Height of the Girder Optimal Simply Supported Girders Subjected to Symmetically Located Vertical Loads. Half-Plane Designs. Case of Two Symmetically located Point Loads Case of Three or More Forces Optimal Simply Supported Girders Subjected to Symmetrically Located Vertical Loads. Full-Plane Designs Selected Classes of Spadal Michell's Structures Girders Carrying the Vertical Loading- Hemp's Structures Transmitting Vertical Forces to a Supporting Column Transmitting a Vertical Force to Supports Around the Vertical Axis Michell's Sphere Shells of Revolution Subjected to Torsion. Case of Arbitrary Meridian optimization of the Meridian The Lightest Conical and Cylindrical Shells The Lightest Conical Shell The Lightest Cylindrical Shell The Least Compliant Systems of Beams Forming a Continuum Layout. hager-Rozvany Grillages Optimum Design of Funiculans and Arc-hgrids Optimal Funiculars-An Elementary Approach The Beam Analogy and the Funicular Equation Constuction of an Optimal Frame 6.2 Rozvany-Prager Approach Towards Optimum Design of Planm Funiculms Archgrids of Least Weight Transmitting a Vertical Force to the Pin Supports on a Contour of a Circle Transmitting a Point Load to Four Supports Forming a Cross Transmitting a Point Load to the Edge of a Simply Supported St ip . Transmitting a Point Load to the Edges Of a Quadrant Transmitting a Point Load to the Boundary of a Square Transmitting a Vertical Distribuled Load to a Simply Supported Boundary Extmsions of the Michell Theory Optimum Design of Trusses. Multiple Loads Trusses of Minimal Weighted Compliance and Fixed Volume Trusses of Minimal Volume. Plastic Design The Methods of Optirnum Design of Shape and Material Inspired by the Theory of Michell Structures In-Plane Loaded Plates of Optimal Thickness: The Variable Thickness Sheet Problem Optimal Choice of Young's Modulus Distribution: The YMD Method 479 Optimal Choice of the Elastic Moduli of a Structure Made of Material of Cubic SymmeĘ: The CMD Method Optimal Choice of the Bulk and Shear Moduli of a Structure Made of an Isotropic Material: The IMD Method Optimum Design of Anisotropy: The AMD Industrial Applications Civil Engineering Structures Inspired by Michell's Solutions Building Designs Based on Michell's Concepts Other Civil Engineering Structures Cable-Stayed, Arch and Deployable Bridges optimal Reinforcement of Concrete Structures Mechanical Engineering Applications, Design Rationalization, Additive Manufacturing hessure Vessels and Containers 2 Applications for Crashworthiness Design Rationalization Additive Manufacturing

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