Plane stress, plane strain, and pure shear at large finite strain

High-speed electrical machines (HSEMs) are becoming more popular in applications such as air handling devices. Using surface-mounted permanent magnet (PM) rotors manufactured from rare earth metals, they provide benefits over their mechanical transmission counterparts. However, these PMs have low tensile strength and are prone to failure under large centrifugal loads when rotating. Therefore, retaining sleeves are used to hold the PMs in compression to eliminate tensile stress and reduce failure risk. The magnets are also often held on a back iron or carrier, forming an assembly of three cylinders. The ability to predict these stresses is extremely important to rotor design. Current published work shows a lack of exploration of analytical methods of calculating these stresses for three-cylinder assemblies. This paper shows the development of plane stress, plane strain and generalised plane strain (GPS) theories for three cylinders. For a range of rotor designs, these theories are compared with finite element analysis (FEA). GPS is shown to be more accurate than plane stress or plane strain for the central region of long cylinders. For short cylinders and for the ends of cylinders, all three theories give poor results.

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CONSIDERATIONS ON NUMERICAL INTEGRATION SCHEMES FOR STIFFNESS MATRICES OF ISOPARAMETRIC ELEMENTS PART I : Equivalence of displacement models using reduced integration with mixed models in plane stress, plane strain and plate bending

Transactions of the Architectural Institute of Japan ◽

10.3130/aijsaxx.314.0_90 ◽

1982 ◽

Vol 314 (0) ◽

pp. 90-101

Author(s):

HISASHI SHIMODAIRA

Keyword(s):

Numerical Integration ◽

Plane Strain ◽

Plane Stress ◽

Mixed Models ◽

Plate Bending ◽

Reduced Integration ◽

Integration Schemes ◽

Stiffness Matrices ◽

Stress Plane ◽

Isoparametric Elements

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Modeling of Stiffness and Strength of Bone at Nanoscale

Journal of Biomechanical Engineering ◽

10.1115/1.4036314 ◽

2017 ◽

Vol 139 (5) ◽

Cited By ~ 16

Author(s):

Diab W. Abueidda ◽

Fereshteh A. Sabet ◽

Iwona M. Jasiuk

Keyword(s):

Plane Strain ◽

Plane Stress ◽

Collagen Fibril ◽

Collagen Matrix ◽

Basic Building Block ◽

Axisymmetric Case ◽

Opposite Trend ◽

Stress Plane ◽

Cohesive Surface ◽

Strength And Stiffness

Two distinct geometrical models of bone at the nanoscale (collagen fibril and mineral platelets) are analyzed computationally. In the first model (model I), minerals are periodically distributed in a staggered manner in a collagen matrix while in the second model (model II), minerals form continuous layers outside the collagen fibril. Elastic modulus and strength of bone at the nanoscale, represented by these two models under longitudinal tensile loading, are studied using a finite element (FE) software abaqus. The analysis employs a traction-separation law (cohesive surface modeling) at various interfaces in the models to account for interfacial delaminations. Plane stress, plane strain, and axisymmetric versions of the two models are considered. Model II is found to have a higher stiffness than model I for all cases. For strength, the two models alternate the superiority of performance depending on the inputs and assumptions used. For model II, the axisymmetric case gives higher results than the plane stress and plane strain cases while an opposite trend is observed for model I. For axisymmetric case, model II shows greater strength and stiffness compared to model I. The collagen–mineral arrangement of bone at nanoscale forms a basic building block of bone. Thus, knowledge of its mechanical properties is of high scientific and clinical interests.

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