Classical music | EPFL Graph Search

Classical music generally refers to the art music of the Western world, considered to be distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" also applies to non-Western art music. Classical music is often characterized by formality and complexity in its musical form and harmonic organization, particularly with the use of polyphony. Since at least the ninth century it has been primarily a written tradition, spawning a sophisticated notational system, as well as accompanying literature in analytical, critical, historiographical, musicological and philosophical practices. A foundational component of Western culture, classical music is frequently seen from the perspective of individual or groups of composers, whose compositions, personalities and beliefs have fundamentally shaped its history. Rooted in the patronage of churches and royal courts in Western Europe, surviving early medieval mus

John-Théodore -alias Jack- Cornaz (1886-1974)

Nadja Maillard

On November the 14th 1974, Jack Cornaz died in Lausanne, the town where he was born in 1886. This study traces the unusual career of this architect – a singular figure in the field of Swiss-French architecture of the twentieth century – whose name, from the 1920s, is associated with a wide range of neo-classical buildings on the shores of Lake Geneva, and analyses its context. Labelled both marginal and a dissident – depending on the standpoint of the critic – Cornaz's production is presented for the first time, through minute exploration of his unpublished archives, extensive information gathered in the course of interviews with numerous protagonists, both near and far, of the "cornazian scene", and comprehensive lateral research. Diversified in terms of quantity, and yet so uniform in terms of typology and program, his production appears consistent enough to express in itself the themes and motives which permit an understanding of both the variety of its expressions and in the unity of its intentions. The analysis of some of its nodal points – types of clients, production under influences, relevance of the old, problematic relationship to the tradition – provides an opportunity to grapple with broader architectural issues, some including ontological dimension : notion of imitation, bound to a style, relations between the architect and his patronage, autobiographical nature of his relation to the object, properties of the settlement... Though considered as a passéiste architect, Cornaz – at least at the start of his career – appreciated a form of modernity, understood as a progressive development of classical and regional types into a new language, which did not reject or betray the heritage of the past. In this respect, his work may be considered as representative of one of those traditionalist tendencies taken into account by the history of architecture over the last two decades. Based on the analytical cataloguing of the architect's archives deposited in the ACM (Archives of Modern Construction, Lausanne), the method applied in this study is a cross-disciplinary approach combining historical research with the principles of anthropological investigation. It is also based upon the interlocking of two propositions : it is a historical inquiry analysing sources as well as an epistemological reflection about cognitive procedures at work in the material in question. Adept at disciplinary nomadism and in mimetic fit with her object, the author applies a "patchwork" method. She is convinced that the effect of contiguity and accumulation is meaningful in itself, and that the interest of this matching of quotations, which leads to admittance for the need of the gaps and interplay of the elements, resides in its unsteadiness, like in a mosaic. The book consists of two closely connected volets. Chapters are thematic in the first one, these theoretical essays are completed with monographs of twenty of J. Cornaz's constructions and catalogue entries for his works.

EPFL2005

Unified formulation for Reissner-Mindlin plates: a comparison with numerical results

Luca Tassinari

Analytical solutions to problems of solids mechanics are useful to test the accuracy and the precision of the numerical approaches. Problems such as shear locking or boundary layer can be better understood with the help of analytical solutions. However, it is known that only simple cases can be solved by hand. Furthermore, some cases which are theoretically solvable can also result in rather tedious analysis. Nowadays computer and mathematical software development allow to avoid this problem if they are associated with a suitable formulation. Classical formulations of mechanics of elastic body solve each particular problem by obtaining standard differential equations but generally do not give a unified method to solve them. In this paper a non-standard formulation is applied to find analytical solutions for elastic plates considering shear deformation (Reissner-Mindlin model) using a computer-aided approach. In addition, the results are compared to finite element model predictions. The main advantage of the proposed methodology over classical approaches is that it can be applied to problems of structural mechanics that are radically different using the same matrix framework, similarly to the FEM. Therefore, a computer-aided approach is used to obtain the analytical solution. This unified formulation is described Tassinari et al. [6]. The Reissner-Mindlin model (Reissner [3], Mindlin [4]) takes into account the shear deformation and it is generally recommended for moderately thick plates whereas Love-Kirchhoff model is more suitable for thin plates (Kirchhoff [1], Love [2]). The derivation of the governing equations of the RM plate results in a system of partial differential equations. The Levy solution technique can be used (Timoshenko and Woinowsky-Krieger [7], Szilard [5]) once the boundary conditions on two opposite edges are given. The solution is written as a series of orthogonal functions of the first coordinate multiplied by unknown functions of the second coordinate. The governing system is reduced to a system of ODEs that applies for each unknown term of the series. The application of the unified formulation to the Reissner-Mindlin plate results in a governing system of ODEs written in a matrix canonical form (see Tassinari et al. [6]). This expression is characterized by the state vector, which contains the generalized stresses and displacements, and the system matrix which describes the equilibrium. It is shown that this form can be applied to several problems of structural mechanics, by consistently adapting both system matrix and state vector. In this paper, the case of the Reissner-Mindlin plate problem with simply support on two opposite edges is solved. The analytical solution for a particular load case is presented showing the differences between the Reissner-Mindlin solution and the predictions given by the Love-Kirchhoff model (Kirchhoff [1], Love [2]). Finally, the vertical displacement field obtained analytically for different thickness-to-side ratios is compared with finite element method predictions. The analytical solution carried out shows the effect of the shear deformation in plate with small slenderness. In particular, the magnitude of this effect is significant for the vertical displacement. In general, the other components of the state vector are not significantly influenced in the domain of the plate but exhibits perturbations close to the edges. This edge effect is known as boundary layer and further investigations are needed considering higher-order terms. The results obtained from the proposed analytical method and numerical models presented in this study are comparable. Furthermore, the finite element analysis carried out shows that for a reasonable mesh refinement the numerical models used give excellent approximation of the analytical solution. Keywords: analytical solution, unified formulation, shell, plate, Reissner-Mindlin, Love-Kirchhoff, shear strain, finite element. References [1] Kirchhoff G., Über das Gleichgewicht und die Bewegungen einer elastischen Scheibe. Journal für reine und angewandte Mathematik, 1850; 40; 51–58. [2] Love, A. E. H., A treatise on the matematical theory of elasticity, Dover, 1944. [3] Mindlin R. D., Influence of rotatory inertia and shear on flexural vibration of isotropic, elastic plates. Journal of Applied Mechanics, 1951; 18; 31–38. [4] Reissner E., The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics, 1945; 67; A69-A77. [5] Szilard R., Theories and applications of plate analysis: classical, numerical and engineering methods. Wiley, 2004. [6] Tassinari L, Monleon S, Gentilini C, Ubertini F. A unified approach for analytical solution of moderately thick shells and plates. (Paper in preparation). [7] Timoshenko S, Woinowsky-Krieger S. Theory of plates and shells. McGraw-Hill, 1959.

IASS Symposium 2009, Valencia, Spain2009

John-Théodore -alias Jack- Cornaz (1886-1974)

Nadja Maillard

EPFL2005

Unified formulation for Reissner-Mindlin plates: a comparison with numerical results

Luca Tassinari

IASS Symposium 2009, Valencia, Spain2009