Advanced Mechanics of Solids

2021 ◽  
Author(s):  
Lester W. Schmerr Jr.
Keyword(s):  
Undergraduate Students ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Mechanics Of Solids ◽  
Stress Strain ◽  
Elastic Bodies ◽  
Mechanics Of Materials ◽  
Modern Textbook ◽  
Elementary Mechanics ◽  
Matrix Vector

Build on the foundations of elementary mechanics of materials texts with this modern textbook that covers the analysis of stresses and strains in elastic bodies. Discover how all analyses of stress and strain are based on the four pillars of equilibrium, compatibility, stress-strain relations, and boundary conditions. These four principles are discussed and provide a bridge between elementary analyses and more detailed treatments with the theory of elasticity. Using MATLAB® extensively throughout, the author considers three-dimensional stress, strain and stress-strain relations in detail with matrix-vector relations. Based on classroom-proven material, this valuable resource provides a unified approach useful for advanced undergraduate students and graduate students, practicing engineers, and researchers.

scholarly journals STRESS-STRAIN STATE OF THE CONICAL SHELL OF VARIABLE THICKNESS BASED ON THREE-DIMENSIONAL EQUATIONS OF ELASTICITY THEORY

2020 ◽  
Vol 82 (2) ◽  
pp. 189-200
Author(s):  
Val.V. Firsanov ◽  
V.T. Pham
Keyword(s):  
Differential Equations ◽  
Classical Theory ◽  
Variable Thickness ◽  
Conical Shell ◽  
Strain State ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Median Surface ◽  
Stress Strain ◽  
Stress Strain State

The results of a study of the stress-strain state of a conical shell of variable thickness based on a non-classical theory are presented. The sought-for displacements of the shell are approximated by polynomials in the normal coordinate to the median surface two degrees higher in relation to the classical theory of the Kirchhoff-Love type. When developing the theory, the three-dimensional equations of the theory of elasticity, as well as Lagrange variational principle are used as the equation of the shell state. As the result of minimizing the specified value of the total energy of the shell, a mathematical model is constructed, which is a system of differential equations of equilibrium in the displacements with variable coefficients and the corresponding boundary conditions. Two cases are considered: the shell is under the action of symmetric and asymmetric loads. Two-dimensional equations are transformed to the system of ordinary differential equations by means of trigonometric sequences as per circumferential coordinate. To solve the formulated boundary value problem, finite difference and matrix sweep methods are applied. The calculations have been made by means of a computer program. After having determined the displacements, shell deformations and tangential stresses are found from geometric and physical equations, transverse stresses - from the equilibrium equations of the three-dimensional theory of elasticity. As an example, a conical shell rigidly restrained at the two edges, with asymmetrically varying thickness is considered. Compared are the results of the VAT calculations obtained as per the improved and classical theories. The significant contribution of additional stresses in the boundary zone to the total stress state of the shell is shown. The received results can be used in the strength and durability calculations and tests of machine-building facilities of various purposes.

scholarly journals Lectures on Solid Mechanics

2008 ◽  
Author(s):  
Claudio Borri ◽  
Michele Betti ◽  
Enzo Marino
Keyword(s):  
Undergraduate Students ◽  
Engineering Students ◽  
Solid Mechanics ◽  
Virtual Work ◽  
Three Dimensional ◽  
Mechanics Of Solids ◽  
Traditional Theory ◽  
Axial Forces ◽  
University Of Florence ◽  
The University

This volume presents the theoretical basics of solid mechanics collecting the lectures held by the Authors for the course of Mechanics of Solids to environmental engineering students at the University of Florence. Lectures on Solid Mechanics is organized in two parts. The first one introduces the theory of three-dimensional elasticity where, after a preparatory synthesis of the basic concepts of mathematics and geometry, the fundamental framework of strain and stress in elastic bodies are introduced. Then the classical law of linear elasticity is presented and finally the part concludes with the "Principle of Virtual Work and variational methods". Moreover, at the end of selected chapters the essential notions of the theory of shells are discussed. The second part concerns the traditional theory of beams focusing on the four fundamental cases: beam under axial forces, terminal couples, torsion, bending and shear. The Readers addressed by this volume are mainly the undergraduate students of Engineering Schools.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

Stress-strain curve of paper revisited

2012 ◽  
Vol 27 (2) ◽  
pp. 318-328 ◽  
Author(s):  
Svetlana Borodulina ◽  
Artem Kulachenko ◽  
Mikael Nygårds ◽  
Sylvain Galland
Keyword(s):  
Three Dimensional ◽  
Strain Curve ◽  
Failure Behavior ◽  
Three Dimensional Model ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Fiber Network ◽  
Bonding Parameters ◽  
Particle Level ◽  
The Impact

Abstract We have investigated a relation between micromechanical processes and the stress-strain curve of a dry fiber network during tensile loading. By using a detailed particle-level simulation tool we investigate, among other things, the impact of “non-traditional” bonding parameters, such as compliance of bonding regions, work of separation and the actual number of effective bonds. This is probably the first three-dimensional model which is capable of simulating the fracture process of paper accounting for nonlinearities at the fiber level and bond failures. The failure behavior of the network considered in the study could be changed significantly by relatively small changes in bond strength, as compared to the scatter in bonding data found in the literature. We have identified that compliance of the bonding regions has a significant impact on network strength. By comparing networks with weak and strong bonds, we concluded that large local strains are the precursors of bond failures and not the other way around.

scholarly journals Using Externally Bonded CFRP to Repair a PCCP with Broken Wires under Combined Loads

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Kejie Zhai ◽  
Hongyuan Fang ◽  
Bing Fu ◽  
Fuming Wang ◽  
Benyue Hu
Keyword(s):  
Prestressed Concrete ◽  
Three Dimensional ◽  
Soil Pressure ◽  
Long Distance ◽  
Stress Strain ◽  
Wire Breakage ◽  
Water Pipelines ◽  
Externally Bonded ◽  
Prestressed Concrete Cylinder Pipe ◽  
Three Dimensional Finite Element

Prestressed concrete cylinder pipe (PCCP) is widely used for long-distance water pipelines throughout the world. However, prestressing wire breakage is the most common form of PCCP damage. For some pipelines that cannot be shut down, a new technique for in-service PCCP repair by externally bonding the pipe with layers of carbon fiber reinforced polymer (CFRP) was proposed. A set of three-dimensional finite element models of the repaired PCCP have been proposed and implemented in the ABAQUS software, which took into account the soil pressure, the weight of the PCCP, the weight of the water, and the hydrostatic pressure. The stress–strain features of the PCCP repaired with CFRP of various thicknesses were analyzed. The stress–strain features of different wire breakage rates for the repaired PCCP were also analyzed. The results showed that the strains and stresses decreased at the springline if the PCCP was repaired with CFRP, which improved the operation of the PCCP. It has been found that the wire breakage rates had a significant effect on the strains and stresses of each PCCP component, but CFRP failed to reach its potential tensile strength when other materials were broken.

Sign in / Sign up

Export Citation Format

Share Document