The stochastic differential calculus for the determination of structural response under wind

1993 ◽  
Vol 48 (2-3) ◽  
pp. 175-188 ◽  
Author(s):  
Gianni Bartoli ◽  
Paolo Spinelli
Keyword(s):  
Differential Calculus ◽  
Structural Response

Contactless Investigation of Nuclear Mechanics of Normal and Lamin Mutant Cells Using a 3D Image- and Model-Based Framework

2009 ◽  
Author(s):  
Paula González ◽  
Michaela Reichenzeller ◽  
Roland Eils ◽  
Evgeny Gladilin
Keyword(s):  
Structural Response ◽  
Nuclear Lamina ◽  
Cell Boundary ◽  
3D Image ◽  
Nuclear Mechanics ◽  
Model Based ◽  
Structural Framework ◽  
External Forces ◽  
Mutant Cells

Apart from storing most of the DNA in eukaryotic cells, the cell nucleus provides mechanical protection through its nuclear envelope to ensure the integrity of the genome. The nuclear lamina is known to play an important role in this respect by supplying a structural framework for the nucleus [1]. The severe diseases arising from mutations in the LMNA gene confirm the importance of the lamin proteins for normal cell functionality [2]. Most experimental techniques for investigation of the cell mechanics are based on the application of external forces onto the cell boundary [3]. Thus, the quantitative determination of the mechanical properties of intracellular structures in situ, still represents a challenging task. In our previous works, we proposed a 3D image- and model-based framework for analysis of intracellular mechanics [4]. In this work, we extend this approach to a fully contactless investigation of nuclear mechanics of normal and LMNA–/– mutant cells. Differently from previous approaches, cellular deformation was induced by chemical agents, i.e., without any mechanical contact with the cell boundary. In particular, we focus on (i) comparative analysis of 3D structural response of nuclear matter with respect to external forces in normal and pathological cell, as well as (ii) determination of the scarcely-investigated nuclear compressibility (i.e. the Poisson’s ratio).

On the curvature of surfaces

1843 ◽  
Vol 4 ◽  
pp. 112-115
Keyword(s):  
Differential Calculus ◽  
Systematic Theory ◽  
Lines Of Curvature ◽  
Umbilical Points ◽  
Analytical Result

The principal object of this paper is, to remove the obscurity in which that part of the theory of the curvature of surfaces which relates to umbilical points has been left by Monge and Dupin, to whom, however, subsequently to the labours of Euler, we are chiefly indebted for a comprehensive and systematic theory of the curvature of surfaces. In it the author shows, that the lines of curvature at an umbilic are not, as at other points on a surface, two in number, or, as had been stated by Dupin, limited; but that they proceed in every possible direction from the umbilic. The obscurity complained of is attributed to the inaccurate conceptions entertained by Monge and Dupin, of the import of the symbol 0/0 in the analytical discussion of this question, the equation which determines the directions of the lines of curvature taking the form 0( dy / dx ) 2 + 0( dy / dx ) + 0 = 0 at an umbilic. After stating that Dupin has been guided by the determination of the differential calculus, the author remarks, that in no case is the differential calculus competent to decide whether 0/0, the form which a general analytical result takes in certain particular hypotheses, as to the arbitrary quantities entering that result, has or has not innumerable values. He then states the principle, that those values of the arbitrary quantities (and none else) which render the equations of condition indeterminate must also render the final result, to which they lead, equally indeterminate; and that, therefore, when such result assumes the form 0/0, its true character is to be tested by the equations that have led to it, after these have been modified by the hypothesis from which that form has arisen.

Time Histories of Wave-in-Deck Loading on Jacket Decks

2006 ◽  
Author(s):  
Katrine van Raaij ◽  
Ove T. Gudmestad
Keyword(s):  
Time Variation ◽  
Structural Response ◽  
Engineering Practice ◽  
Offshore Platforms ◽  
Wave Loading ◽  
Extreme Wave ◽  
Incoming Wave ◽  
Time Histories ◽  
The Difference

Most researchers agree that wave-in-deck loading is of dynamic nature and that the dynamic effects on the structural response are important. However, there exists no engineering practice for the determination of load time histories for waves hitting the decks of fixed offshore platforms. This applies to both the time variation and the magnitude of the loading. This paper presents the main recommendations for wave-in-deck loading with reference to wave tank experiments of a model of the Statfjord A Condeep platform subjected to extreme wave loading. The recommendations for loading from these tests comprise time variation as well as magnitude. These recommendations are used as a basis to suggest a simplified method to estimate wave-in-deck loading on jacket platform decks, for which, to the difference from Condeep platforms, the wave height amplification due to the interaction between the incoming wave and the structure (Swan et al., 1997) is negligible. The resulting ‘recipe’ for wave-in-deck time histories on North Sea jacket platforms is compared to relevant results previously reported in the literature. The method is categorised as a ‘global’ approach, that is, one uses an effective deck area as opposed to a detailed deck model. The method is suggested to be applicable for analyses where a ‘rough but reasonable’ estimate for wave-in-deck loading is sufficient.

scholarly journals Note on the Determination of Centres of Curvature

1915 ◽  
Vol 18 ◽  
pp. 207-210
Author(s):  
J. M'Whan
Keyword(s):  
Differential Calculus ◽  
Plane Curve ◽  
Radius Of Curvature ◽  
Circular Functions

For determining the Cartesian co-ordinates of the centre of curvature of a plane curve two methods are principally used in the text-books. One of these (see for example, Edwards, “Differential Calculus,” p 266, § 339) having previously established the formula for the radius of curvature, derives the coordinates of the centre of curvature by using the circular functions of the angle “ψ,” which the tangent to the curve at the point considered makes with OX. Since, however, for the same tangent, and therefore the same “ψ” the curve may be either convex or concave towards OX (and accordingly the centre of curvature have quite different positions), this method introduces an essential ambiguity, and is not to be recommended.

scholarly journals Estimation of damage severity using sparse static measurement

2015 ◽  
Vol 23 (2) ◽  
pp. 213-221 ◽  
Author(s):  
Ivana ŠTIMAC GRANDIĆ ◽  
Davor GRANDIĆ
Keyword(s):  
Structural Damage ◽  
Structural Response ◽  
Estimation Procedure ◽  
Simple Arithmetic ◽  
Damage Scenarios ◽  
Severity Estimation ◽  
Influence Line ◽  
Single Sensor ◽  
Grey Relation Coefficient

A new structural damage estimation procedure using grey relation coefficient and curvature of displacement influence line in beams using sparse measurement is proposed in this paper. The method is based on static structural response which can be obtained using single sensor. Determination of damage location as well as determination of corre­sponding damage severity can be easily calculated with simple arithmetic operations, which is the main advantage of the proposed method. Conducted numerical simulation for different damage scenarios and various measurement sparseness and experimental validation confirm the effectiveness of proposed damage severity estimation procedure.

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