Mathematical modeling of the stress state of an orthotropic piezoelectric material with a spheroidal cavity under internal pressure

Abstract Protection against local failure is one of the integral components in the design-by-analysis requirements in ASME BPVC Section VIII, Division 2. Of the methods offered by the ASME, the Local Strain Limit procedure outlined in 5.3.3.1 is the typical calculation method. However, it has been found that relying on this procedure alone can lead to untenable utilization results if used on certain analyses with varied load paths. The flange described in this study was calculated using “design by analysis” according to Part 5 of ASME BPVC Section VIII, Division 2. The elastic-plastic stress analysis method was used. The flange was loaded with an initial bolt pre-tension and then with internal pressure. During the local failure calculation, an abnormal condition was encountered in the form of a large spike in the history curve of the ratio between plastic strain and limiting triaxial strain. An investigation found that despite being in a stress state below yield stress, some nodes had a non-zero plastic strain and high triaxiality factor. This was caused by the load sequence: first, the bolt pre-tension and then internal pressure. The flange was first bent due to the pre-tension load, and later experienced bending in the opposite direction after the internal pressure load was applied. This resulted in a relatively low stress state with a high triaxiality factor and non-zero plastic strain in certain areas, which then showed high utilization under the local failure strain limit criterion. This paper will discuss how this issue can be avoided by using the strain limit damage calculation procedure 5.3.3.2 outlined in ASME BPVC Section VIII, Division 2.

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Programming curvilinear paths of flat inflatables

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1904544116 ◽

2019 ◽

Vol 116 (34) ◽

pp. 16692-16696 ◽

Cited By ~ 6

Author(s):

Emmanuel Siéfert ◽

Etienne Reyssat ◽

José Bico ◽

Benoît Roman

Keyword(s):

Inverse Problem ◽

Stress State ◽

Internal Pressure ◽

Minimal Model ◽

Thin Sheets ◽

Inflatable Structures ◽

Deployable Structures ◽

Application Potential ◽

Numerical Tool ◽

Target Path

Inflatable structures offer a path for light deployable structures in medicine, architecture, and aerospace. In this study, we address the challenge of programming the shape of thin sheets of high-stretching modulus cut and sealed along their edges. Internal pressure induces the inflation of the structure into a deployed shape that maximizes its volume. We focus on the shape and nonlinear mechanics of inflated rings and more generally, of any sealed curvilinear path. We rationalize the stress state of the sheet and infer the counterintuitive increase of curvature observed on inflation. In addition to the change of curvature, wrinkles patterns are observed in the region under compression in agreement with our minimal model. We finally develop a simple numerical tool to solve the inverse problem of programming any 2-dimensional (2D) curve on inflation and illustrate the application potential by moving an object along an intricate target path with a simple pressure input.

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Ultimate stress state of a plate made of orthotropic material under uniform internal pressure

Journal of Physics Conference Series ◽

10.1088/1742-6596/1425/1/012116 ◽

2019 ◽

Vol 1425 ◽

pp. 012116

Author(s):

N S Blokhina

Keyword(s):

Stress State ◽

Internal Pressure ◽

Orthotropic Material ◽

Ultimate Stress

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Experimental investigation of the stress state of a coiled shell under the action of internal pressure

Strength of Materials ◽

10.1007/bf01523439 ◽

1978 ◽

Vol 10 (9) ◽

pp. 1050-1055

Author(s):

P. G. Pimshtein ◽

E. G. Borsuk

Keyword(s):

Experimental Investigation ◽

Stress State ◽

Internal Pressure

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Study of strain-stress state of flat knives for cutting thin-walled pipes

Ferrous Metallurgy Bulletin of Scientific Technical and Economic Information ◽

10.32339/0135-5910-2021-9-1039-1046 ◽

2021 ◽

Vol 77 (9) ◽

pp. 1039-1046

Author(s):

S. P. Eron’ko ◽

E. V. Oshovskaya ◽

O. A. Kovaleva

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Stress State ◽

Mathematical Simulation ◽

Cross Section ◽

Cutting Tool ◽

Small Diameter ◽

Pipe Welding ◽

Strain Stress ◽

Thin Walled

Cutting of pipes into measured lengths on-line of pipe welding mill by disc saws and by facilities of abrasive cutting requires special measures of safety of personal. Besides, the necessity of frequent change of cutting instrument results in losses of production time. To eliminate the drawbacks, a study was initiated related to creation of shears which could enable to accomplish a quality transverse cutting of thin-walled pipes of small diameter by flat knives with various form of the working edges. A methodology and the results of study of strain-stress state of flat knives with application of physical and mathematical simulation of the process of transverse cutting of thin-walled pipes of small diameter presented. At the physical simulation using a polarization-optical installation, the pictures of deformation centers arising in the lower part of the knife in the zone of contact of its cutting edges with the body of the hollow circular profile being cut by it were obtained. In the experiment, models of three types of knives made of organic glass on a scale of 1:1 were used. Cutting edges of the knives for cutting pipes of 25 mm outer diameter, wall thickness of 2 mm were wedge-shaped, convex semicircular and concave. The data from studies of the loaded state of transparent knife models served as the basis for mathematical simulation of the strain-stress state of the shears cutting tool in the SolidWork application package using a strength analysis module that implements the finite element method in the form of tetrahedrons. The current values of the pipe cutting force used in the mathematical model were preliminarily calculated according to the previously proposed dependence, taking into account the strength of the hollow profile material and the area of the cut layer of its cross section for a given relative displacement of the cutting edges of the knife. The results of mathematical modeling were the pictures of deformations and equivalent stresses of the cutting part of the knife, determined according to the third theory of strength. A qualitative similarity has been established for the distribution patterns of stress fields recorded using the polarization-optical method on knife models and obtained in mathematical modeling for working samples of the shears cutting tool operated under the conditions of pipe welding mills. The proposed mathematical model makes it possible to estimate the values of the maximum equivalent stresses in the working part of a flat knife, taking into account the shape of its cutting edges, as well as the force required for cutting a thin-walled pipe into measured lengths with the corresponding dimensions of its cross-section and the strength of the material.

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