Fractional Differential Equations

https://orbilu.uni.lu/bitstream/10993/13726/1/phu-meshless.pdf

Review: Meshless methods: A review and computer implementation aspects

Minimum Design Loads for Buildings and Other Structures provides requirements for general structural design and includes means for determining dead, live, soil, flood, wind, snow, rain, atmospheric ice, and earthquake loads, as well as their combinations, which are suitable for inclusion in building codes and other documents. This Standard, a revision of ASCE/SEI 7-05, offers a complete update and reorganization of the wind load provisions, expanding them from one chapter into six. The Standard contains new ultimate event wind maps with corresponding reductions in load factors, so that the loads are not affected, and updates the seismic loads with new risk-targeted seismic maps. The snow, live, and atmospheric icing provisions are updated as well. In addition, the Standard includes a detailed Commentary with explanatory and supplementary information designed to assist building code committees and regulatory authorities. Standard ASCE/SEI 7 is an integral part of building codes in the United States. Many of the load provisions are substantially adopted by reference in the International Building Code and the NFPA 5000 Building Construction and Safety Code. Structural engineers, architects, and those engaged in preparing and administering local building codes will find this Standard an essential reference in their practice. Note: New orders are fulfilled from the second printing, which incorporates the errata to the first printing.

Minimum Design Loads for Buildings and Other Structures

Surface roughness has a huge impact on many important phenomena. The most important property of rough surfaces is the surface roughness power spectrum C(q). We present surface roughness power spectra of many surfaces of practical importance, obtained from the surface height profile measured using optical methods and the atomic force microscope. We show how the power spectrum determines the contact area between two solids. We also present applications to sealing, rubber friction and adhesion for rough surfaces, where the power spectrum enters as an important input.

/pdf/on-the-nature-of-surface-roughness-with-application-to-finn99eaoj.pdf

On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion.

http://www.multiscaleconsulting.com/publications/Contact_mechanics_for_randomly_rough_surfaces.pdf

Contact mechanics for randomly rough surfaces

One of us recently developed a theory of contact mechanics for randomly rough surfaces [B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001)]. In this paper we compare the results of the analytical model with (exact) numerical results. We also present some analytical results related to the theory.

/pdf/elastic-contact-between-randomly-rough-surfaces-comparison-3p55l3d837.pdf

Elastic contact between randomly rough surfaces: Comparison of theory with numerical results

The nominal tensile strength of concrete structures is constant for relatively large sizes, whereas it decreases with the size for relatively small sizes. When, as usually occurs, the experimental investigation does not exceed one order of magnitude in the scale range, a unique tangential slope in the bilogarithmic strength versus size diagram is found. On the other hand, when the scale range extends over more than one order of magnitude, a continuous transition from slope −1/2 to zero slope may appear. This means that for smaller scales a self-similar distribution of Griffith cracks is prevalent, whereas for larger scales the disorder is not visible, the size of the defects and heterogeneities being limited. In practice there may be a dimensional transition from disorder to order. The assumption of multifractality for the damaged material microstructure represents the basis for the so-called multifractal scaling law. This is a best-fit method that imposes the concavity of the bilogarithmic curve upwards, in contrast to the size effect law of Bažant. The relevant results in the literature for ranges in scale extending over more than one order of magnitude are analysed.

Size effects on nominal tensile strength of concrete structures: multifractality of material ligaments and dimensional transition from order to disorder

The mechanical properties of concrete are highly dependent on the types and proportions of binders and aggregates. Because existing equations for predicting the modulus of elasticity as a function of compressive strength are obtained from experiments performed on a restricted number of concrete specimens subjected to uniaxial compression, the existing equations cannot cover the entire experimental data. In this study, more than 3000 data sets obtained by many investigators using various materials have been collected and analyzed statistically in order to develop a reliable new equation for elastic modulus of concrete. The compressive strengths of the considered concretes range from 40 to 160 MPa (5.8 to 23.2 ksi). The new equation also takes into consideration the types of coarse aggregates and mineral admixtures. The proposed formula should be effective in the design of both normal strength concrete and high strength concrete structures.

A Practical Equation for Elastic Modulus of Concrete

Experimental evidence of the fractality of fracture surfaces has been widely recognized in the case of concrete, ceramics and other disordered materials. An investigationpost mortem on concrete fracture surfaces of specimens broken in direct tension has been carried out, yielding non-integer (fractal) dimensions of profiles, which are then related to the ‘renormalized fracture energy’ of the material. No unique value for the fractal dimension can be defined: the assumption of multifractality for the damaged, material microstructure produces a dimensional increment of the dissipation space with respect to the number 2, and represents the basis for the so-called multifractal scaling law. A transition from extreme Brownian disorder (slope 1/2) to extreme order (zero slope) may be evidenced in the bilogarithmic diagram: the nominal fracture energyGF increases with specimen size by following a nonlinear trend. Two extreme scaling regimes can be identified, namely the fractal (disordered) regime, corresponding to the smallest sizes, and the homogeneous (ordered) regime, corresponding to the largest sizes, for which an asymptotic constant value ofGF is reached.

Bernardino Chiaia

Papers

Elastic contact between randomly rough surfaces: Comparison of theory with numerical results

Size effects on nominal tensile strength of concrete structures: multifractality of material ligaments and dimensional transition from order to disorder

A Practical Equation for Elastic Modulus of Concrete

Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy

Progressive collapse of framed building structures: Current knowledge and future prospects