Visual representation of the kinematics of the continuum
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The purpose of this paper is to present some experimentally determined properties of the continuum. The development starts with the illustration of deformed shapes, or metamorphoses, and the introduction of the concept of displacement. From there on, the development follows the classic mechanics-of-continuum presentation, spatial and time derivatives of displacement, strains, stresses and rigid rotations. To unify the presentation, all considerations are applied to the case of a circular ring subjected to diametral compression. Particular advantage is taken of grids, moiré, brittle-coatings and photoelasticity methods to obtain the physical representations of the properties. The following loci are considered: isokinetics, isothetics, isogonics, isoclinics of displacement, displacement trajectories, loci of partial derivative, isogyros, isotenics, isochromatics, isoclinics of strain and stress, isostatics, isopachics, isobars, isostrophics and isoentatics. The understanding of the properties of these fields helps in the visualization of the mechanics of the continuum, in general, and may prove to be particularly useful in the fields of plasticity and finite strain.
KeywordsMechanical Engineer Fluid Dynamics Partial Derivative Time Derivative Visual Representation
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- 1.Vasarhelyi, D., “Contribution to the Calculation of Stresses from Photoelastic Values,”Proc. SESA, IX (1),27–34 (1951).Google Scholar
- 2.O'Regan, R., “New Method for Determining Strain on the Surface of a Body with Photoelastic Coatings,”Experimental Mechanics,5 (8),241–246 (1965).Google Scholar
- 3.Post, D., “A New Photoelastic Interferometer Suitable for Static and Dynamic Measurements,”Proc. SESA, XII (1),99–116 (1955).Google Scholar
- 4.Drouven, G., “Measurement of the Sum of the Principal Stresses in Plane Problems of Elasticity by Interference,” Doctoral Thesis, Washington University (1952).Google Scholar
- 5.Post, D., “Photoelastic Evaluation of Individual Principal Stresses by Large Field Absolute Retardation Measurements,”Proc. SESA, XIII (2),119–132 (1956).Google Scholar
- 6.Tesar, V., “Representation simple et complète en grandeur et direction, des efforts intérieurs,”Génie Civil,98 (28),615–619 (1931).Google Scholar