Elastic/Plastic Discs Under Plane Stress Conditions by Sergey Alexandrov

By Sergey Alexandrov

This quantity offers a unified method of calculate the airplane pressure distribution of pressure and pressure in skinny elastic/plastic discs topic to numerous loading stipulations. there's a huge volume of literature on analytical and semi-analytical strategies for such discs obeying Tresca’s yield criterion and its linked stream rule. nevertheless, so much of analytical and semi-analytical ideas for Mises yield criterion are according to the deformation thought of plasticity. A exotic function of the recommendations given within the current quantity is that the circulate conception of plasticity and Mises yield criterion are followed. The ideas are semi-analytical within the feel that numerical equipment are just essential to review usual integrals and clear up transcendental equations. The booklet indicates that less than yes stipulations recommendations according to the deformation and stream theories of plasticity coincide. the entire strategies are illustrated with numerical examples. The objective of the publication is to supply the reader with a imaginative and prescient and an perception into the issues of study and layout of elastic/plastic discs. the constraints and the applicability of recommendations are emphasised. The e-book is written for engineers, graduate scholars and researchers attracted to the improvement of innovations for research and layout of skinny elastic/plastic discs.

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Example text

5 > acr disc. 3. The distributions of the radial and circumferential stresses are depicted in Figs. 9 for several values of ρc . The distributions of the radial, circumferential and axial strains are shown in Figs. 12 for the same values of ρc . The solid lines correspond to the total strains and the broken lines to the plastic strains. 8) Substituting Eq. 4) into Eq. 30) [1 + η1 (η1 + η)] . It is convenient to consider the cases η1 ≤ 1 and η1 > 1 separately. Firstly, it is assumed that η1 ≤ 1.

69) . Here ψm is the value of ψc at q = qm . 69) should be solved for ψm numerically. Then, the value of ρc at q = qm denoted by ρm is determined from Eq. 63) as ρm a 2 = (2 + ηη1 ) sin ψm + η1 4 − η2 cos ψm − 2qm 4 − η2 η1 η sin ψm + 4 − η2 cos ψm − 2 sin ψm . 70) In the elastic region, a ≤ Υ ≤ ρm , the distributions of the strains follow from Eq. 60) in the form εθe εr Am (1 + ν) εθ Am (1 + ν) εre = = = =− + B + Bm (1 − ν) , − ν) , (1 m 2 k k k k Υ Υ2 εze εz = = −2ν Bm . 71) k k Having found ψm and ρm from Eqs.

In this case, the value of ψe is determined from Eq. 12)1 as ψe = π − arcsin √ 3 1 − a2 . 13) Thus the value of ψe is in the range 5π /6 ≤ ψe < π when a varies in the range 0 ≤ a < 1. Therefore, cos ψe < 0 and it follows from Eq. 7) that dψa /dq < 0 at ψa = ψe . Differentiating Eq. 11) for ρc with respect to q yields √ π dψc dρc2 = 3 sec2 + ψc . dq 6 dq It is reasonable to assume that dρc /dq > 0. Therefore, dψc /dq > 0. Finally, it is possible to conclude that the value of ψ varies in the range ψa ≤ ψ ≤ ψc .

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