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Coursecode: wb1409
Coursename: Theory of Elasticity
DUT creditpoints: 2
ECTS creditpoints: 3
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Faculty
of Mechanical
Engineering and Marine Technology
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Lecturer(s): Keulen, prof.dr.ir. A.
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Tel.: 015-27 86515
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Catalog
data:
Stress and strain tensors, elastic constitutive equations, linear theory of
elasticity, energy principles, energy theorems, stress functions, composite
theory, homogenization
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Course
year: MSc 1st
year
Semester: 1A / 1B
Hours p/w: 2
Other hours: 2
Assessment: Exercises + oral exam
Assessm.period(s): By appointm.
(see academic calendar)
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Prerequisites: wb1410
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Follow
up: wb1400,
b20, wb1402A, wb1402B, wb1405A,
wb1405B
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Detailed
description of topics:
This course deals
with the theory of elastic deformations of continuous bodies, including a
number of important engineering applications. This field is the actual basis
of essentially all strength of materials tools in mechanical engineering,
marine technology and aerospace engineering. The elastic behaviour of
engineering materials can, as a first approximation, often be considered to
be linear and then determines the flexibillity of structures and the
allowable stresses, as long as in-elastic behaviour (plasticity and creep) or
facture does not occur. This course intends to deepen the knowledge of
elastic deformations of engineering components build up during the first and
second year courses. At the same time, it is the starting point for advanced
courses on elasticity such as those dealing with buckling of structures, or
plates and shells. Following a brief review of the fundamental notions from
continuum mechanics, the general three-dimensional theory for elastic
boundary value problems is developed. From this, the governing equations for
the linear theory are deduced. Then, a number of important energy principles
are discussed, which form the basis for numerical methods for problems of
elasticity, in particular the finite element method. Subsequently, the
analytical solutions for a number of typical two- and three-dimensional
elasticity problems are discussed in depth. The elastic behaviour of
composite materials is discussed, with emphasis on the internal state in the
composite. Finally, the theory for large elastic deformations is considered
for application to rubber materials.
The contents of the course are as follows:
Review of continuum mechanics: strain-displacement relations,
equilibrium conditions, (thermo-) elastic constitutive equations;
Energy principle of the linear theory of elasticity: potential
energy; complementary energy; mixed principles; relation with Rayleigh-Ritz
methods;
Two-dimensional elastic problems: equations of Navier-Cauchy; stress
functions; stress concentrations; cracks, stress intensity factors;
Three-dimensional elastic problems: thick-walled tubes/spheres;
stress concentration around spherical hole; contact; wave propagation;
Inhomogeneous materials: inclusions; inhomogeneities;
Finite strain elasticity: hyperelastic material.
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Course
material:
Specific parts
from:
- Y.C. Fung, Foundations of
Solid Mechanics, Prentice Hall, New York, 1965.
- M.E. Gurtin, An Introduction
to Continuum Mechanics, Mathematics in Science and Engineering, vol.
158, Academic Press, New York, 1982.
- I.S. Sokolnikoff,
Mathematical Theory of Elasticity, McGrawHill, 2nd ed., New York, 1956.
- R.W. Ogden, Nonlinear elastic
deformations, Ellis Horwood Ltd., 1984.
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References
from literature:
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Remarks
(specific information about assesment, entry requirements, etc.):
Oral examination
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Goals:
The objective of this course is to offer a sound basis for the treatment of a
wide range of problems of elasticity. To that end, the governing equations of
the theory of elasticity are discussed, based on general continuum mechanics,
and specific methods of solution are considered for the linear theory.
The solution of a number of typical engineering elasticity problems are
pressented in detail, partly to illustrate the adopted solution strategy, and
partly because they provide model problems that are key to several related
fields of engineering.
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Computer
use:
Most applications of the theory of elasticity require numerical techniques.
This course includes the common basic concepts on which the Finite Element
Method is based. Specific numerical aspects are dealt with in b20.
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Laboratory
project(s):
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Design
content:
The theory of elasticity is the foundation for the analysis of stresses and
the flexibility in the design of structures and components. This holds for
the initial design stages, where "rough" estimates are made based
on simple models (beams, etc.), as well as for the final, detailed designs
where advanced numerical tools are used.
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Percentage
of design: 50%
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