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13 Dynamic, One-Dimensional and Miscellaneous Problems
The previous part of this monograph makes it clear that the branch of the Mathematical Theory of Contact Mechanics, which deals with quasistatic...
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6 Mathematical Preliminaries
Part II provides mathematical formulations of the models, the assumptions that underlie them, their weak or variational formulations and the...
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11 Contact with Wear or Adhesion
In this chapter we present results on models of frictional contact when the wear of the contacting surfaces is taken into account. The importance of...
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3 Additional E.ects Involved in Contact
More is involved in contact than just friction, although it is the main process. Indeed, during a contact process elastic or plastic deformations of...
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1 Introduction
Considerable progress has been achieved recently in modeling and mathematical analysis of various processes involved in contact between deformable...
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6 Stepwise Inflation of a Balloon
When we inflate a balloon in the usual manner, namely by blowing air into it by mouth, we first inhale deeply by expanding our lungs. After that we...
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9 Stability of the Spherical Shape
Ever so often we observe that a balloon, which is spherical in the undistorted state, becomes elongated upon inflation so that we obtain a...
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Out-of-Plane Vibrations of Plane Frames
The frame vibrations studied in Chaps. 3 to 5 are for in-plane vibrations. If a plane frame acted upon by a force or horizontal ground vibration in...
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Conical Shells of Linearly Varying Thickness Subjected to Normal Loads
The equilibrium equations for a surface element of a conical shell in the framework of generalized plane stress of linear theory of elasticity are...
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Dumbbell Model for Dilute and Semi-Dilute Solutions
Dumbbell models are very crude representations of polymer molecules. Too crude to be of much interest to a polymer chemist, since it in no way...
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Equilibrium Statistics: Monte Carlo Methods
Monte Carlo methods use random numbers, or ‘random’ sequences, to sample from a known shape of a distribution, or to extract distribution by other...
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Vibrations of X-Braced Multi-Story Frames
The study of vibrations for the x-braced portal frames in the last chapter is extended to high-rise x-braced multi-story frames in this chapter....
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Vibrations of Frames with Inclined Members
The model established for the vibration of the inclined bars in the last chapter now is applied to two- and three-bar frames with inclined members.
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11 Random Vibrations of Large Finite Element Systems
The basic idea for the computation of the stochastic response is based on the Karhunen-Loève expansion of the stochastic loading. For each Karhunen-...
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4 Finite Element Method
In this chapter, the fundamentals of the displacement-based finite element method are reiterated in a concise form, details can be found in a number...
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5 Non-Linear Static Analysis
The state of the art in the capability to predict the stability behavior of shell structures refers to areas such as asymptotic analysis [69] and...
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7 Rational Treatment of Uncertainties
Structural analysis up to this date, generally is still based on a deterministic conception. Observed variations in loading conditions, material...
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9 Direct Monte Carlo Simulation
The evaluation of the stochastic response by the Monte Carlo simulation technique is a powerful method for highly nonlinear systems as well as for...
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A Imperfection Data Bank
For the stochastic modeling of geometric imperfections as described in Sec. 12.1, a database [5] has been available. This database provides...