scholarly journals Mechanics based statistical prediction of structure size and geometry effects on safety factors for composites and other quasibrittle materials

2008 ◽  
Vol 35 (1-3) ◽  
pp. 53-71 ◽  
Author(s):  
Zdeněk Bazant
Keyword(s):  
Mathematical Description ◽  
Structural Strength ◽  
Journal Article ◽  
Statistical Prediction ◽  
Probability Density Distribution ◽  
Safety Factors ◽  
Statistical Parameters ◽  
Size And Shape ◽  
Quasibrittle Materials ◽  
Nominal Strength

The objective of this paper1 is a rational determination of safety factors of quasibrittle structures, taking into account their size and shape. To this end, it is necessary to establish the probability density distribution function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf's of the nominal strength of structure are known to be Gaussian and Weibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. This recent result is reviewed, and then mathematically extended in two ways: 1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and 2) to a mathematical description of the statistical parameters of the pdf of structural strength as a function of structure size and shape. Experimental verification and calibration is relegated to a subsequent journal article.

Adequate Strength for Small High-Speed Vessels

1968 ◽  
Vol 5 (01) ◽  
pp. 63-71
Author(s):  
Philip J. Danahy
Keyword(s):  
Stress Analysis ◽  
High Speed ◽  
Structural Strength ◽  
Integrated Approach ◽  
Suggested Method ◽  
Impact Loads ◽  
Analysis Method ◽  
Safety Factors ◽  
Recreational Vessels

The paper presents a method for the determination of the critical minimum scantlings for small high-speed vessels. Particular attention is given to the shell plating strength for hydrodynamic impact loads. The suggested method uses an integrated approach involving assumed loads, suggested safety factors, and preferred stress-analysis method. The stress analysis uses plastic theory based partly on the works of J. Clarkson and Thein Wah. Included in the paper is a comparison of the relative structural strength of several commercial, military, and experimental hydrofoil vessels along with a few planing boats and a seaplane hull. This shows the variation of existing vessel structures and compares them to the results obtained by the suggested method. Most commercial, military, and recreational vessels exceed the minimum scantlings of the suggested method. The most significant deviation is the hull of the seaplane:

scholarly journals Comparative Study on Non-Gaussian Characteristics of Wind Pressure for Rigid and Flexible Structures

2018 ◽  
Vol 2018 ◽  
pp. 1-26 ◽  
Author(s):  
Lei Jiang ◽  
Jin-hua Li ◽  
Chun-xiang Li
Keyword(s):  
Empirical Formula ◽  
Flexible Structures ◽  
Wind Pressure ◽  
Windward Side ◽  
Leeward Side ◽  
Flexible Structure ◽  
Probability Density Distribution ◽  
Statistical Parameters ◽  
Rigid Structure ◽  
Non Gaussian

This paper summarizes a comprehensive study for non-Gaussian properties of wind pressure. The field measurements are implemented on the structure surface of a rigid structure, while a large-span membrane structure is selected as the flexible structure wind pressure contrast group. The non-Gaussian characteristics of measured pressure data were analyzed and discussed through probability density distribution, characteristic statistical parameters, power spectral density function, and the correlations, respectively. In general, the non-Gaussian characteristics of wind pressure present depending on tap location, wind direction, and structure geometry. In this study, the fluctuating wind pressures on the windward side and leeward side of the structures show obvious different degrees of non-Gaussian properties; that is, the surface of rigid structure shows strong non-Gaussian property in leeward, while the roof of flexible structure shows obvious non-Gaussian property in windward. Finally, this paper utilizes the present autospectrum empirical formula to fit the wind pressure power spectrum density of the measured data and obtains the conclusion that the existing empirical formula is not ideal for fitting of the flexible structure.

scholarly journals The mechanical strength of side-to-side tendon repair with mismatched tendon size and shape

2014 ◽  
Vol 40 (3) ◽  
pp. 239-245 ◽  
Author(s):  
J. Fridén ◽  
T. F. Tirrell ◽  
S. Bhola ◽  
R. L. Lieber
Keyword(s):  
Ultimate Load ◽  
Tendon Repair ◽  
Cadaver Study ◽  
Safety Factors ◽  
Contraction Force ◽  
Size And Shape ◽  
Pronator Teres ◽  
Flexor Carpi Ulnaris ◽  
Extensor Carpi Radialis ◽  
Mismatched Donor

Tendon transfers frequently require coaptation of two mismatched tendons. In this cadaver study, ultimate load, stiffness, and Young’s modulus were measured in tendon-to-tendon attachments with mismatched donor and recipient tendons, using pronator teres (PT) to extensor carpi radialis brevis (ECRB) and flexor carpi ulnaris (FCU) to extensor digitorum communis (EDC). FCU-to-EDC attachments failed at higher loads than PT-to-ECRB attachments, but they had similar modulus and stiffness values. Ultimate tensile strength of the tendon attachments exceeded the maximum predicted contraction force of any of the transferred muscles, with safety factors of four-fold for the FCU-to-EDC and two-fold for the PT-to-ECRB transfers. This implies that size and shape mismatches should not be contraindications to tendon attachment in transfers. The strength safety factors suggest that postoperative immobilization of these transfers is unnecessary.

scholarly journals Scaling of Quasi-Brittle Fracture and the Fractal Question

1995 ◽  
Vol 117 (4) ◽  
pp. 361-367 ◽  
Author(s):  
Zdeneˇk P. Bazˇant
Keyword(s):  
Size Effect ◽  
Composite Laminates ◽  
Process Zone ◽  
Asymptotic Properties ◽  
Material Strength ◽  
Fractal Nature ◽  
Quasibrittle Materials ◽  
Large Size ◽  
Fracture Simulation ◽  
Nominal Strength

The paper represents an extended text of a lecture presenting a review of recent results on scaling of failure in structures made of quasibrittle materials, characterized by a large fracture process zone, and examining the question of possible role of the fractal nature of crack surfaces in the scaling. The problem of scaling is approached through dimensional analysis, the laws of thermodynamics and asymptotic matching. Large-size and small-size asymptotic expansions of the size effect on the nominal strength of structures are given, for specimens with large notches (or traction-free cracks) as well as zero notches, and simple size effect formulas matching the required asymptotic properties are reported. The asymptotic analysis is carried out, in general, for fractal cracks, and the practically important case ofnonfractal crack propagation is acquired as a special case. Regarding the fractal nature of crack surfaces in quasibrittle materials, the conclusion is that it cannot play a signification role in fracture propagation and the observed size effect. The reason why Weibull statistical theory of random material strength does not explain the size effect in quasibrittle failures is explained. Finally, some recent applications to fracture simulation by particle models (discrete element method) and to the determination of size effect and fracture characteristics of carbon-epoxy composite laminates are briefly reviewed.

Scaling Of Fracture In Quasibrittle Materials And The Question Of Possible Influence Of Fractal Morphology

1995 ◽  
Vol 409 ◽  
Author(s):  
Zdeněk P. Bažant
Keyword(s):  
Size Effect ◽  
Asymptotic Expansions ◽  
Asymptotic Properties ◽  
Fractal Nature ◽  
Nonlinear Fracture Mechanics ◽  
Quasibrittle Materials ◽  
Large Size ◽  
Nonlinear Fracture ◽  
Nominal Strength ◽  
Asymptotic Matching

AbstractThe paper presents a review of recent results on the problem of size effect (or the scaling problem) in nonlinear fracture mechanics of quasibrittle materials and on the validity or recent claims that the observed size effect may be caused by the fractal nature of crack surfaces. The problem of scaling is approached through dimensional analysis and asymptotic matching. Large-size and small-size asymptotic expansions of the size effect on the nominal strength of structures are presented, considering not only specimens with large notches (or traction-free cracks) but also structures with no notches. Simple size effect formulas matching the required asymptotic properties are given. Regarding the fractal nature of crack surfaces, it is concluded that it cannot be the cause of the observed size effect.

scholarly journals The Effect of Low Concentrations of Bedload on the Erosion Pattern and the Structural Strength of Rigid Force Mains

2010 ◽  
Vol 4 (1) ◽  
pp. 105-115
Author(s):  
Hillel Rubin ◽  
Dmitry Tokarev ◽  
Holger Schüttrumpf
Keyword(s):  
Safety Factor ◽  
Structural Strength ◽  
Construction Safety ◽  
Domestic Sewage ◽  
Solid Particles ◽  
Safety Factors ◽  
Pipe Failure ◽  
Low Concentrations ◽  
History Of ◽  
Service Curve

This manuscript concerns the decrease of the structural strength and possible collapse of force (pressure) mains due to bedload erosion (abrasion), caused by low concentrations of hard solid particles transported with the sanitary sewage. Such a phenomenon may probably occur in combined sanitary systems (CSS), but it has also been observed in force mains delivering domestic sewage, due to occasional penetration of hard solid particles into the sanitary sewerage system. Force mains are usually subject to stresses originating from the internal pressure combined with those of the external load. For the design of such pipelines, Schlick's formula is usually applied. The present study applies Schlick's formula to represent the pipe failure curve. Then by properly introducing safety factors into Schlicks' formula the study defines service curves of the pipe. Each service curve is associated with a particular value of the pipe construction safety factor. In the next step by applying the concept of service curves the study hypothesizes the extension of Schlick's formula for possible calculation of the decrease of the pipe safety factor due to the presence of the invert groove. Calculations are made by using the ANSYS code, and the numerical results are applied to evaluate a particular case history of an asbestoscement (AC) force main collapse.

Size Effect Law and Critical Distance Theories to Predict the Nominal Strength of Quasibrittle Structures

2013 ◽  
Vol 65 (2) ◽  
Author(s):  
Pere Maimí ◽  
Emilio V. González ◽  
Narcís Gascons ◽  
Lluís Ripoll
Keyword(s):  
Size Effect ◽  
Structural Strength ◽  
Critical Distance ◽  
Cohesive Law ◽  
Nominal Strength ◽  
Critical Fracture ◽  
Open Hole ◽  
Cracked Structures ◽  
Nonuniform Stress Field

The design of structures with a nonuniform stress field is of great industrial interest. The ability of the size effect law and critical distance theories to predict the nominal strength of notched and open hole specimens is analyzed in the present paper. The results obtained with these methods are compared with the solution of the problem computed, taking into account the material cohesive law. A conclusion of this paper is that the role of the critical fracture energy in determining the structural strength is negligible, except in large cracked structures. For unnotched structures of any size and for small cracked structures, the key parameter is the initial part of the softening cohesive law. This allows us to define design charts that relate the structural strength to a specimen size normalized with respect to a material characteristic length.

Unbiased estimation of particle number and sizes using the new stereological tools: the disector, the fractionator, the selector, and the nucleator — or just point-sampled intercepts

1988 ◽  
Vol 46 ◽  
pp. 428-429
Author(s):  
H.J.G. Gundersen
Keyword(s):  
Particle Number ◽  
Small Distance ◽  
Parallel Plane ◽  
Unbiased Estimation ◽  
Severe Problem ◽  
New Era ◽  
Size And Shape ◽  
Distinct Property ◽  
Sectioned Tissue

Previously, all stereological estimation of particle number and sizes were based on models and notoriously gave biased results, were very inefficient to use and difficult to justify. For all references to old methods and a direct comparison with unbiased methods see recent reviews.The publication in 1984 of the DISECTOR, the first unbiased stereological probe for sampling and counting 3—D objects irrespective of their size and shape, signalled the new era in stereology — and give rise to a number of remarkably simple and efficient techniques based on its distinct property: It is the only known way to obtain an unbiased sample of 3-D objects (cells, organelles, etc). The principle is simple: within a 2-D unbiased frame count or sample only cells which are not hit by a parallel plane at a known, small distance h.The area of the frame and h must be known, which might sometimes in itself be a problem, albeit usually a small one. A more severe problem may arise because these constants are known at the scale of the fixed, embedded and sectioned tissue which is often shrunken considerably.

The influence of confocal microscope design on imaging performance

1993 ◽  
Vol 51 ◽  
pp. 144-145
Author(s):  
C J R Sheppard
Keyword(s):  
Image Quality ◽  
Fluorescence Imaging ◽  
Confocal Microscope ◽  
Industrial Applications ◽  
Three Dimensions ◽  
Design Parameters ◽  
Weak Signals ◽  
Size And Shape ◽  
Imaging Performance ◽  
Fundamental Limitation

The confocal microscope is now widely used in both biomedical and industrial applications for imaging, in three dimensions, objects with appreciable depth. There are now a range of different microscopes on the market, which have adopted a variety of different designs. The aim of this paper is to explore the effects on imaging performance of design parameters including the method of scanning, the type of detector, and the size and shape of the confocal aperture.It is becoming apparent that there is no such thing as an ideal confocal microscope: all systems have limitations and the best compromise depends on what the microscope is used for and how it is used. The most important compromise at present is between image quality and speed of scanning, which is particularly apparent when imaging with very weak signals. If great speed is not of importance, then the fundamental limitation for fluorescence imaging is the detection of sufficient numbers of photons before the fluorochrome bleaches.

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