By Sing C. Tang and Jwo Pan
Functioning as an creation to fashionable mechanics ideas and numerous purposes that take care of the technological know-how, arithmetic and technical points of sheet steel forming, this e-book information theoretically sound formulations in response to ideas of continuum mechanics for finite or huge deformation, which could then be carried out into simulation codes. The forming strategies of complicated panels through desktop codes, as well as broad useful examples, are recreated during the many chapters of this ebook on the way to gain training engineers by means of aiding them greater comprehend the output of simulation software program.
desk of Contents
1. creation to commonplace car Sheet steel Forming methods
2. Tensor, pressure, and pressure
three. Constitutive legislation
four. Mathematical versions for Sheet steel Forming tactics
five. skinny Plate and Shell Analyses
6. Finite point equipment for skinny Shells
7. equipment of answer and Numerical Examples
eight. Buckling and Wrinkling Analyses
concerning the Authors
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Additional resources for Mechanics Modeling of Sheet Metal Forming
25) Based on Eq. 26) p . 4 Yield Functions Under Multiaxial Stresses The uniaxial stress-strain relation from a tensile test gives the initial yield stress 00. The initial yield stress is an important material property that usually is listed in material handbooks. However, the material elements in the structural members under plastic deformation usually are not subjected to the uniaxial stress state. Instead, the material elements often are subjected to multiaxial loading conditions. Therefore, we need to determine the yield behavior under multiaxial loading conditions.
10. The reference configuration represents the solid occupied at time t= 0. The current configuration represents the solid occupied at time t. We consider a material point P a s shown in the figure. The material point P a t time 0 has a position vector X, which defines the material coordinates Xl, X2, and X3 for point P. The material point Pmoves to a new position P' at time t. Now the material point P h a s a new position vector x, which defines the spatial coordinates xl, x2,and x3 for the material point P.
Because the traction vector T is in the same direction of the unit normal vector n, we can write T = n . 3) Here, oprepresents the principal stress or the eigenvalue of the stress tensor Q. In the component form, where 6jk represent the Kronecker delta. 5 represents three equations for the three components nj. 9) Here, I,,12,and I3 are independent of the coordinate system chosen. They are called the invariants of the stress tensor CT. 13) Tensor, Stress, and Strain I 25 Because CT is real and symmetric (oij= oji), we will have three real roots (eigenvalues) that are called the principal stresses.