1.

Record Nr.

UNINA9910865258003321

Autore

Öchsner Andreas

Titolo

Plasticity Theory : Yield Conditions in the Invariant Space

Pubbl/distr/stampa

Cham : , : Springer, , 2024

©2024

ISBN

9783031588716

9783031588709

Edizione

[1st ed.]

Descrizione fisica

1 online resource (102 pages)

Collana

SpringerBriefs in Applied Sciences and Technology Series

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

Intro -- Preface -- Contents -- Symbols and Abbreviations -- Latin Symbols (Capital Letters) -- Latin Symbols (Small Letters) -- Greek Symbols (Small Letters) -- Mathematical Symbols -- Special Matrices -- Indices, Superscripted -- Indices, Subscripted -- Abbreviations -- 1 Fundamentals -- 1.1 Comments on the Stress Matrix -- 1.2 Graphical Representation of Yield Conditions -- References -- 2 Experimental Realization of Multiaxial Stress States -- 2.1 Thin-Walled Tubes Under Internal/External Pressure and Additional Loads -- 2.2 Loading Devices with Two or Three Axes -- 2.3 Hydrostatic Pressure Due to a Pressure Chamber and Additional Loads -- References -- 3 Yield Conditions -- 3.1 Fundamentals -- 3.2 Mises Yield Condition -- 3.3 Tresca Yield Condition -- 3.4 Drucker-Prager Yield Condition -- 3.5 Willam-Warnke Three-Parameter Yield Condition -- 3.6 Additional Components of the Constitutive Law -- 3.6.1 Flow Rule -- 3.6.2 Hardening Rule -- References -- 4 Elasto-Plastic Finite Element Simulations -- 4.1 Approach for One-Dimensinal Problems -- 4.1.1 Integration of the Material Equations -- 4.1.2 Derivation of the Fully Implicit Backward-Euler Algorithm for Isotropic Hardening -- 4.1.3 Derivation of the Fully Implicit Backward-Euler Algorithm for Kinematic Hardening -- 4.1.4 Derivation of the Fully Implicit Backward-Euler Algorithm for Combined Hardening -- 4.1.5 Derivation of the Semi-Implicit Backward-Euler Algorithm for Isotropic Hardening -- 4.2 Approach for Three-



Dimensional Problems -- 4.2.1 Differentiation of the Yield Conditions -- 4.2.2 Derivation of the Fully Implicit Backward Euler Algorithm for Isotropic Hardening -- References -- Index.

2.

Record Nr.

UNINA9910153655203321

Autore

Tubbs Robert

Titolo

Hilbert's Seventh Problem : Solutions and Extensions / / by Robert Tubbs

Pubbl/distr/stampa

Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2016

ISBN

981-10-2645-9

Edizione

[1st ed. 2016.]

Descrizione fisica

1 online resource (IX, 85 p. 1 illus.)

Collana

IMSc Lecture Notes in Mathematics, , 2509-8098

Disciplina

510.9

Soggetti

Mathematics

History

Functional analysis

Integral equations

Number theory

History of Mathematical Sciences

Functional Analysis

Integral Equations

Number Theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Chapter 1. Hilbert's seventh problem: Its statement and origins -- Chapter 2. The transcendence of e; and ep -- Chapter 3. Three partial solutions -- Chapter 4. Gelfond's solution -- Chapter 5. Schneider's solution -- Chapter 6. Hilbert's seventh problem and transcendental functions -- Chapter 7. Variants and generalizations.

Sommario/riassunto

This exposition is primarily a survey of the elementary yet subtle innovations of several mathematicians between 1929 and 1934 that led to partial and then complete solutions to Hilbert’s Seventh Problem (from the International Congress of Mathematicians in Paris, 1900). This volume is suitable for both mathematics students, wishing to experience how different mathematical ideas can come together to



establish results, and for research mathematicians interested in the fascinating progression of mathematical ideas that solved Hilbert’s problem and established a modern theory of transcendental numbers. .