scholarly journals Elastic machines: A non standard use of the axial shear of linear transversely isotropic elastic cylinders

2020 ◽  
Vol 185-186 ◽  
pp. 57-64
Author(s):  
Fahmi Grine ◽  
Giuseppe Saccomandi ◽  
Makrem Arfaoui
Keyword(s):  
Transversely Isotropic ◽  
Axial Shear ◽  
Elastic Cylinders

The transverse compression of anisotropic fibre monofilaments

1965 ◽  
Vol 285 (1401) ◽  
pp. 275-286 ◽  
Keyword(s):  
Polyethylene Terephthalate ◽  
Contact Area ◽  
Reasonable Agreement ◽  
Synthetic Fibre ◽  
Transversely Isotropic ◽  
Transverse Compression ◽  
Oriented Films ◽  
Elastic Cylinders ◽  
Transverse Modulus ◽  
Microscope Stage

A synthetic fibre monofilament was compressed between transparent fiats mounted on a microscope stage, and an image of the contact area thrown onto a screen. The contact area was determined as a function of load for polyethylene terephthalate, polypropylene and nylon monofilaments. These monofilaments can be regarded as transversely isotropic elastic cylinders and show considerable anisotropy, the extensional modulus being at least six times the transverse modulus. A theoretical solution was therefore derived for the contact area of a cylinder compressed between two rigid planes when the cylinder is a transversely isotropic elastic body. The solution is given in terms of the elastic constants, the radius of the cylinder and the applied load and was found to hold experimentally. The theory was used together with measurements of Poisson’s ratio and extensional modulus to derive the transverse modulus of the filaments from the compression experiments. In polyethylene terephthalate and polypropylene the calculated moduli are in reasonable agreement with those obtained directly from uniaxially oriented films.

The compression of anisotropic fibre monofilaments. II

1966 ◽  
Vol 291 (1425) ◽  
pp. 267-278 ◽  
Keyword(s):  
Elastic Constants ◽  
Poisson’S Ratio ◽  
Synthetic Fibre ◽  
Transversely Isotropic ◽  
Elastic Cylinder ◽  
Poisson's Ratio ◽  
Elastic Cylinders ◽  
Complete Specification ◽  
Microscope Stage

A synthetic fibre monofilament was compressed between transparent flats mounted on a microscope stage. The change in the monofilament diameter parallel to the plane of the flats was determined as a function of load for polyethylene terephthalate and nylon monofilaments. These monofilaments can be regarded as transversely isotropic elastic cylinders. A theoretical solution was therefore derived for the change in diameter of a transversely isotropic elastic cylinder compressed between two rigid parallel planes. The solution for the change in diameter in terms of the elastic constants and the applied load was verified experimentally. Measurements of the change in diameter as a function of load were combined with measurements of the width of the contact zone between the cylinder and the upper transparent flat. The results together with subsidiary measurements of extensional compliance and extensional Poisson’s ratio were then used to derive the transverse compliance and the transverse Poisson’s ratio of the monofilaments. This compression problem provides the first reported determination of the transverse Poisson’s ratio for synthetic fibre monofilaments. It is therefore now possible to obtain all five independent elastic constants, four of which are related to the measurements described in this paper. For the sake of completeness, results for the torsional compliance of these monofilaments have been undertaken thus giving complete specification of the elastic properties.

Reverse time migration in tilted transversely isotropic media

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Razec Cezar Sampaio Pinto da Silva Torres ◽  
Leandro Di Bartolo
Keyword(s):  
Seismic Anisotropy ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computer Clusters ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Tti Media

ABSTRACT. Reverse time migration (RTM) is one of the most powerful methods used to generate images of the subsurface. The RTM was proposed in the early 1980s, but only recently it has been routinely used in exploratory projects involving complex geology – Brazilian pre-salt, for example. Because the method uses the two-way wave equation, RTM is able to correctly image any kind of geological environment (simple or complex), including those with anisotropy. On the other hand, RTM is computationally expensive and requires the use of computer clusters. This paper proposes to investigate the influence of anisotropy on seismic imaging through the application of RTM for tilted transversely isotropic (TTI) media in pre-stack synthetic data. This work presents in detail how to implement RTM for TTI media, addressing the main issues and specific details, e.g., the computational resources required. A couple of simple models results are presented, including the application to a BP TTI 2007 benchmark model.Keywords: finite differences, wave numerical modeling, seismic anisotropy. Migração reversa no tempo em meios transversalmente isotrópicos inclinadosRESUMO. A migração reversa no tempo (RTM) é um dos mais poderosos métodos utilizados para gerar imagens da subsuperfície. A RTM foi proposta no início da década de 80, mas apenas recentemente tem sido rotineiramente utilizada em projetos exploratórios envolvendo geologia complexa, em especial no pré-sal brasileiro. Por ser um método que utiliza a equação completa da onda, qualquer configuração do meio geológico pode ser corretamente tratada, em especial na presença de anisotropia. Por outro lado, a RTM é dispendiosa computacionalmente e requer o uso de clusters de computadores por parte da indústria. Este artigo apresenta em detalhes uma implementação da RTM para meios transversalmente isotrópicos inclinados (TTI), abordando as principais dificuldades na sua implementação, além dos recursos computacionais exigidos. O algoritmo desenvolvido é aplicado a casos simples e a um benchmark padrão, conhecido como BP TTI 2007.Palavras-chave: diferenças finitas, modelagem numérica de ondas, anisotropia sísmica.

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