173,764 research outputs found
Suncoast Ritz Building, C
No full textThe Suncoast Ritz building exterior.https://digitalcommons.usf.edu/gandy_street/5292/thumbnail.jp
Ritz Variational Method for the Flexural Analysis of Rectangular Kirchhoff Plate on Winkler Foundation
No full textIn this study, the Ritz variational method has been applied to solve the bending problem of rectangular Kirchhoff plate resting on Winkler foundation for the case of simply supported edges and transverse distributed load. The problem was presented in variational form using energy principles to obtain the total potential energy functional. Ritz technique was then used to find the generalised displacement parameters which minimized the total potential energy functional; where basis functions were choose to apriori satisfy the boundary conditions. Analytical solutions were obtained which were found to be identical with Navier’s series solutions for the general case of arbitrary distributed transverse load, as well as the specific cases of point loads, sinusoidal load, uniform and linearly distributed loads
The use of positive and negative penalty functions in solving constrained optimization problems and partial differential equations
No full textThe Rayleigh-Ritz Method together with the Penalty Function Method is used to investigate the use of different types of penalty parameters. The use of artificial springs as penalty parameters is a very well established procedure to model constraints in the Rayleigh-Ritz Method, the Finite Element Method and other numerical methods. Historically, large positive values were used to define the stiffness coefficient of artificial springs, until recent publications demonstrated that it is possible to use negative values to define the stiffness coefficients of the springs. Furthermore, recent publications show that constraints can be enforced using positive and negative mass or inertia in vibration problems and in a more generic sense using eigenpenalty parameters which are penalty parameters in the matrix associated with the eigenvalue. Before the commencement of this thesis, solutions using artificial inertia were published only for beams and simple spring-mass systems.
In this thesis the use of all possible types of penalty parameters are investigated in vibration problems of Euler-Bernoulli beams, thin plates and shallow shells and in elastic stability analysis of Euler-Bernoulli beams, including penalty parameters associated with the geometrical stiffness matrix. The study includes the use of penalty parameters for both enforcing support boundary conditions and continuity conditions along structural joints.
This investigation started with the selection of the set of admissible functions that would: (a) allow modelling of beams, plates and shells in completely free boundary conditions; (b) not present any limitation in the number of functions that can be used in the solution. This gives the possibility to converge to the constraint solution and to model any type of boundary conditions.
The procedure proposed in this work combines several advantages: accuracy of the results, relative fast convergence, simplicity of the set of admissible functions and flexibility to define boundary conditions. While there are other procedures that may give better accuracy for specific cases, the proposed method is more widely applicable.
The procedure used in this work also includes a way to check for round-off errors and ill-conditioning in the results; as well as a way to bracket the exact solution with upper and lower-bound results
Biotic and Abiotic Controls on Calcium Carbonate Formation in Soils
No full textOver half of the carbon (C) taking part in the global C cycle is held in terrestrial systems.
Because of the sensitivity of the C cycle to changes in such soil-based pools of carbon, it is
important to understand the basic mechanisms by which soil C is stored and cycled between the
range of di erent pools which occur belowground. In the context of climate change mitigation,
it is considered that increasing soil-based stocks of C, either by reducing losses from soils, or by
actively sequestering new carbon, is a potentially important strategy . Organic carbon is the
main form of carbon in soil and as such has received most focus. Cont/d.Milodowski, Antoni (supervisor British Geological Survey
Decadal Migration of Dome C Inferred by Global Navigation Satellite System Measurements
No full textUnderstanding the behaviour of domes under both contemporary and historical environmental conditions is essential to facilitate the study of dome-divide dynamics and the interpretation of ice core records. This paper presents nearly 20 years of GNSS observations at Dome C in East Antarctica, focusing on ice velocity and accumulation rates. The 38 measuring poles established in 1996 for the EPICA Dome C project were surveyed three times in 18 years. The data analysis indicates alterations in ice velocity patterns, including a horizontal velocity shift across the dome and a dynamic summit migration of about 100 m a-1. Specifically, increases in velocity on the southeastern slope were counterbalanced by a similar reduction in the northwestern sector. These changes are likely related to variations in accumulation distribution as indicated by snow radar measurements and shifts in the drainage basin of the Byrd Glacier. Furthermore, a 10% alteration in snow accumulation rates at Dome C over the past decade compared with previous centuries was observed, accompanied by an elevation increase of about 3.5 mm a-1. The recent findings of the BE-OI project highlight the minimal perturbations of the climate signal on the ice core, attributable to glaciological variability at the dome position
Ritz-type projectors with boundary interpolation properties and explicit spline error estimates
No full textIn this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and we provide a priori error estimates for them. The abstract analysis is exemplified by considering spline spaces and we equip the corresponding error estimates with explicit constants. This complements our results recently obtained for explicit spline error estimates based on the classical Ritz projectors in (Numer Math 144(4):889-929, 2020)
Orton and Spooner Ritz Cinema Opening
No full textGeorge Orton, Sons and Spooner Limited works photograph showing opening ceremony for Ritz Cinema - left C. J. Spooner, centre George Orton and Mrs. Anne Orton, right Tom Orton
Generalization Error in the Deep Ritz Method with Smooth Activation Functions
No full textDeep Ritz method is a deep learning paradigm to solve partial differential equations. In this article we study the generalization error of the Deep Ritz method. We focus on the quintessential problem which is the Poisson’s equation. We show that generalization error of the Deep Ritz method converges to zero with rate C√n , and we discuss about the constant C. Results are obtained for shallow and residual neural networks with smooth activation functions.Peer reviewe
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates
No full textIn this work, the Ritz variational method for solving the flexural problem of Kirchhoff–Love plates under transverse distributed load has been presented systematically in matrix form. An illustrative application of the matrix presentation was done for simply supported rectangular Kirchhoff–Love plate under uniformly distributed load. The application used a one term Ritz approximating displacement (coordinate, or basis) function. A one term Ritz approximate solutions obtained for center displacement of square plates showed a difference of 1.9 % from the exact solution for displacement. Solution obtained for the bending moment at the center showed a difference of 7.9 % from the exact solution for bending moment. The one term Ritz approximation for the maximum shear force showed a difference of –10.7 % from the exact solution. The results obtained for a one term Ritz approximation of the displacement shape function was reasonably close for practical purposes
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