By Sergey Alexandrov
This quantity provides a unified method of calculate the aircraft rigidity distribution of rigidity and pressure in skinny elastic/plastic discs topic to varied loading stipulations. there's a gigantic volume of literature on analytical and semi-analytical suggestions for such discs obeying Tresca’s yield criterion and its linked move rule. nonetheless, so much of analytical and semi-analytical ideas for Mises yield criterion are in keeping with the deformation concept of plasticity. A exotic function of the recommendations given within the current quantity is that the circulation idea of plasticity and Mises yield criterion are followed. The ideas are semi-analytical within the feel that numerical tools are just essential to review usual integrals and remedy transcendental equations. The publication exhibits that lower than yes stipulations strategies in line with the deformation and movement theories of plasticity coincide. the entire strategies are illustrated with numerical examples. The target of the publication is to supply the reader with a imaginative and prescient and an perception into the issues of research and layout of elastic/plastic discs. the constraints and the applicability of strategies are emphasised. The publication is written for engineers, graduate scholars and researchers drawn to the advance of strategies for research and layout of skinny elastic/plastic discs.
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Additional resources for Elastic/Plastic Discs Under Plane Stress Conditions
2 2 ρc Here B has been eliminated by means of Eq. 81). It is convenient to put ψ0 = ψa = p and ρ0 = a in Eqs. 57). Then, ρ = a exp 3β1 (ψ − ψa ) 2 sin (ψa − π/3) . 84) It follows from this equation and the definition for ψc that ρc = a exp 3β1 (ψc − ψa ) 2 sin (ψa − π/3) . 85) Solving Eq. 83) for ρc and A gives ρc2 = 3β0 − 3β12 sin (ψc + π/6) , β1 sin (ψc − π/3) A = 3β12 sin ψc + π − 3β0 .
1007/978-3-319-14580-8_2 27 28 2 Mechanical Loading It is worthy of note that the enlargement of a hole in plates or discs is one of the classical problems in plasticity. Solutions to this problem for various material models are contained in textbooks and monographs [1–4]. A recent review of available solutions for the enlargement of a circular hole in thin plates has been given in . 5) Substituting Eq. 4) into Eq. 31) results in 1 − a2 qe = √ . 5) Since the plastic zone starts to develop from the inner radius of the disc, the material is elastic in the range ρc ≤ ρ ≤ 1.
65) 46 2 Mechanical Loading Differentiating Eq. 66) (2 − ηη1 ) cos ψc + η1 4 − η2 sin ψc + (2 − ηη1 ) sin ψc − η1 4 − η2 cos ψc d ρ 2 c + . a2 dψc Differentiating Eq. 67) (2 − ηη1 ) cos ψc + η1 4 − η2 sin ψc (2 − ηη1 ) . [1 + η1 (η1 − η)] (2 − ηη1 ) sin ψc − η1 4 − η2 cos ψc Using Eqs. 67) the right hand side of Eq. 65) is found as a function of ψc . The solution of Eq. 68) η2 η1 4 − η2 cos ψ + (ηη1 − 2) sin ψ where η2 = η12 − 1 . 1 + η1 (η1 − η) The procedure for finding the strains is as follows.
Elastic/Plastic Discs Under Plane Stress Conditions by Sergey Alexandrov