Download Encyclopedia of Physics (Principles of Classical Mechanics by S. Flugge (edited) PDF

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Extra info for Encyclopedia of Physics (Principles of Classical Mechanics and Field Theory) - Volume III 1

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However, for the sake of simplicity, Xo is given here as a prescribed constant. l [10], where two kinds of probability distributions are partially jointed at a specific boundary of x Xo. This type of combined distribution is well fitted to the case where measured data in the upper and lower region of the distribution are ruled by different factors as in, for instance, the annual maximum wind speed in a specific district. In general, the annual maximum speed is composed of those of typhoon and seasonal wind.

LO. It can be observed that FA improves IS markedly. 67 X 10- 3 X Ll = 85kN, L3 = 65kN, L2 = 75kN, L4 = 55kN, X L5 = 45kN, L7 = 2000kN L6 = 35kN, Ls = 2000kN CONCLUSIONS In the proposed approach, a fitting-adaptive density function is introduced to calculate the failure probability instead of the importance sampling density function, while the importance sampling density function is only used for generating sample points. This approach is very effective when the sample size is small, it is therefore useful for time-consuming problems.

In[I-P{xJl =N{xJ ... 1) -In[(I-P{xJ)(1-P{xj})l=N{xJ+ N{xj} ... (16) indicates that the occurrence numbers are approximately equal to the exceedance probabilities. This deformation is done in order to compare the relations among load combination methods, especially to compare MTR method with LC and PC methods. 2), we can obtain the following relations. 2) 32 Computational Stochastic Mechanics Exceedance Events [ {S,+B} {s,} U {Bj} {r,+B} U {rj+sJ {r,+r} {rJ U {rj} {rm,+s}U{r"li+sJ {rm,+r"li} {rmJ U {r"li} {rm,+rj} U {r"li+rJ 1 de Morgan's Law : ({B}U{BJ>"={S/n{BJ" Derming Functions of Safety [ UIB,+Sjl UIs,IUIBjl UIr, + sjlUIrj + s,l UIr,+rjl UIr,lUIrjl UIrm,+SjlUIr"li+s,1 UIrm' + r"lil UIrm,IUIr"lil UIrm' + rjlUIr"li + r,l 1 1) Exceedance Probabilities: EIUIx,ll= I-P{xJ , EIUIx,IUIxjll=(1-P{xJ)(l-P{x}) 2) Transformation to Occurrence Number Domain: -In[1-P{xJI = N{xJ , -In[(1-P{xJ)(1-P{xj})1 = N{xJ+ N{x} Occurrence Numbers [ N{Si+Sj} N{s,} + N{B) N{r,+B}+N{rj+B,} N{ri+r} N{rJ+N{r} N{rm,+B}+N{r"li+BJ N{rm,+r"li} N{rmJ + N{r"Ii} N{rm,+r}+N{r"li+rJ {Si+Sj} means the event r«Si+Sj) UIXi+Xj] means the step function U(r-(xi+x}).

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