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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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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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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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Momentum and Energy Relations
The equations of motion (5.12) for the charged insulating sphere of radius a moving with arbitrary center velocity u(t) can be rewritten in...
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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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Applications of the Correlation Length
The correlation length is the system–dependent parameter, which defines the structure of the dominant current–carrying (electric or fluid) paths....
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Pressure Saturation Curves and the Critical Volume Fraction for Percolation
The pressure-saturation curves of porous media give fundamental information about the pore space. In equilibrium, ignoring effects due to hysteresis,...
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Effects of Multi-Scale Heterogeneity
It is generally agreed that problems with multi-scale heterogeneity present the biggest challenge to computation and understanding. A few such...
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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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Derivation of Force and Power Equations
The inconsistency between the power and force equations of motion, (2.4) and (2.1) or (2.5), is so surprising that one is tempted to question the...
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Internal Binding Forces
In Appendix B, we have critically confirmed the evaluation of the self electromagnetic force and power, (3.1) and (3.2), leading to the force and...
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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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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...
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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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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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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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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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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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3 Spectral Analysis of Finite Dimensional Operators
A great number of engineering problems can be viewed as an input to output map**, as shown in Fig. 3.1, where the system represents the law for the...