Finite area element snow loading prediction - applications and advancements

1992 ◽  
Vol 42 (1-3) ◽  
pp. 1537-1548 ◽  
Author(s):  
Scott L. Gamble ◽  
Will W. Kochanski ◽  
Peter A. Irwin
Keyword(s):  
Finite Area ◽  
Area Element ◽  
Snow Loading

scholarly journals Effects of roof size, heat transfer, and climate on snow loads: studies for the 1995 NBC

1995 ◽  
Vol 22 (4) ◽  
pp. 770-784 ◽  
Author(s):  
P. A. Irwin ◽  
S. L. Gamble ◽  
D. A. Taylor
Keyword(s):  
Heat Transfer ◽  
Size Effect ◽  
Heat Loss ◽  
Large Area ◽  
Finite Area ◽  
Area Element ◽  
Snow Load ◽  
Snow Loads ◽  
Flat Roofs ◽  
Element Method

As roof sizes increase, the ability of the wind to reduce the uniform snow loads is diminished, thus resulting in higher uniform loads. Results of recent research into this size effect and the influence of heat loss through roofs in four Canadian cities (St. John's, Montreal, Saskatoon, and Edmonton) using the finite area element method are described and snow load formulae for uniform loads on large roofs are proposed. Also, the drift loading on lower roofs adjacent to large area upper roofs has been studied using similar techniques, and revised formulae for the peak loading in the drift at the step are put forward taking into account the size of the upper roof and the presence of parapets. The snow load provisions developed in this paper have been proposed for the 1995 edition of the National Building Code. Key words: snow loads, drift loads, uniform loads, large flat roofs, size effect, heat loss, finite area element method, computational fluid dynamics.

A New and Simpler Formulation for Radiative Angle Factors

1963 ◽  
Vol 85 (2) ◽  
pp. 81-87 ◽  
Author(s):  
E. M. Sparrow
Keyword(s):  
Numerical Evaluation ◽  
Energy Exchange ◽  
Analytical Calculation ◽  
Additional Benefit ◽  
Finite Area ◽  
Reduced Order ◽  
Practical Utility ◽  
New Formulation ◽  
Superposition Theorem

A new representation for diffuse angle factors has been derived which replaces the usual area integrals by more tractable contour (i.e., line) integrals. The new formulation generally simplifies analytical calculation of angle factors. The advantages of the new representation are associated with the reduced order of the integrals (i.e., double reduced to single, quadruple reduced to double) which must be evaluated to calculate the angle factor. An additional benefit of the new representation is that integrals of simpler form are encountered than in the present representation. For the numerical evaluation of angle factors, the reduction in the order of the integrals should have great practical utility. In the case of energy exchange between an infinitesimal element and a finite area, a superposition theorem has been derived which permits results for certain basic surfaces to be linearly combined to yield angle factors for surfaces at other orientations. Several illustrations of the application of the new formulation are presented.

scholarly journals Hermite interpolation by piecewise polynomial surfaces with polynomial area element

2017 ◽  
Vol 51 ◽  
pp. 30-47 ◽  
Author(s):  
Michal Bizzarri ◽  
Miroslav Lávička ◽  
Zbyněk Šír ◽  
Jan Vršek
Keyword(s):  
Hermite Interpolation ◽  
Piecewise Polynomial ◽  
Area Element

scholarly journals A Polyakov Formula for Sectors

2017 ◽  
Vol 28 (2) ◽  
pp. 1773-1839 ◽  
Author(s):  
Clara L. Aldana ◽  
Julie Rowlett
Keyword(s):  
Heat Kernel ◽  
Explicit Expression ◽  
Unit Area ◽  
Logarithmic Singularity ◽  
Conformal Factor ◽  
Opening Angle ◽  
Conformal Deformation ◽  
Finite Area ◽  
Different Parts

Abstract We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmic singularity at the origin. We compute explicitly all the contributions to this formula coming from the different parts of the sector. In the process, we obtain an explicit expression for the heat kernel on an infinite area sector using Carslaw–Sommerfeld’s heat kernel. We also compute the zeta-regularized determinant of rectangular domains of unit area and prove that it is uniquely maximized by the square.

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