# Continuum Mechanics A & B and Exercises

Muhlhaus, Hans-Bernd (2001). Continuum Mechanics A & B and Exercises.

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Title Continuum Mechanics A & B and Exercises The present manuscript is an updated version of the lecture notes I had used in 1993 for lectures at Gifu University and the TU Delft. I will update this introduction as the lecture evolves. At this stage I have revised Section 1 on Vectors and Tensors. The main difference to the previous manuscript is that I have taken out the subsection on covariant differentiation, Christoffel symbols etc in acknowledgement of the fact that if curve-linear coordinates are used it is usually either is in a numerical context (iso-parametric finite elements), or one restricts oneself to cylindrical or spherical coordinates. In both cases the full differential calculus in curve-linear coordinates is not needed. However this does not mean that the ability to express geometric transformations in Lagrangian coordinates (which are curve-linear in general) is unnecessary. Quite the contrary, some of the basic geometric relationships derived in Section 1 will be very useful e.g. in the construction of constitutive relationships and the interpretation of various well-known definitions of stress and strain tensors. Accordingly we begin with a brief representation of vectors, tensors in curvilinear coordinates, whereby the curvilinear coordinates are the deformed material coordinates. The present lecture series is again intended for students who have already had their first encounter with continuum mechanics. I begin with a brief representation of vectors, tensors and equations of motion in curvilinear coordinates, whereby the curvilinear coordinates may be the deformed material coordinates. Continuum mechanicsCurvelinear coordinatesConstraintsStressStrainCosserat continuumPath independent integrals 2001-01-01 290501 Mechanical Engineering230111 Geometry280210 Simulation and Modelling290704 Geomechanics249999 Physical Sciences not elsewhere classified230110 Calculus of Variations and Control Theory290800 Civil Engineering290801 Structural Engineering Muhlhaus, Hans-Bernd Other AE Green and W Zerna (1968) Theoretical Elasticity, Oxford at the Clarendon Press.

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