Nanobeam Theory Taking Into Account Physical Nonlinearity View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2020-07-14

AUTHORS

V. A. Krysko, I. V. Papkova, M. V. Zhigalov, A. V. Krysko

ABSTRACT

In this paper, we construct a new theory of nanobeams taking into account the dependence of the material properties on the stress state. The theory is based on the Euler–Bernoulli kinematic model in the first approximation. The beam material is isotropic but heterogeneous. For the first time, the physical nonlinearity and the dependence of the material properties on the temperature are taken into account in the study of nanobeams, and the theory is developed for arbitrary materials. It is based on the theory of small elasticplastic strains and on the the modified torque theory of elasticity. The stationary temperature field is determined by solving the three-dimensional Poisson equation with boundary conditions of orders 1–3. The initial equations are derived from the Hamilton–Ostrogradskii principle. The desired system of partial differential equations is reduced to the Cauchy problem by the finite difference method of the second order of accuracy, and the Cauchy problem is solved by the Runge–Kutta or Newmark method. At each time step, an iterative procedure is developed by the Birger method of variable elasticity parameters. The stationary solution follows from the dynamic solution of the problem obtained by the method of determination (the method of the parameter position). The convergence of the solution is investigated depending on the number of points of partition along the length and thickness of the beam in the finite difference method as well as on the method of solving the Cauchy problem and the size-dependent parameter, i.e., the solution of the problem is considered to have almost infinite number of degrees of freedom. Numerical examples are given for a beam rigidly clamped at the ends with the stress-strain diagram for aluminum. Accounting for the size-dependent parameter in the nanobeam theory significantly affects the load-carrying capacity of nanobeams. More... »

PAGES

522-529

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11182-020-02065-9

DOI

http://dx.doi.org/10.1007/s11182-020-02065-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1129355922


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Yurii Gagarin State Technical University of Saratov, Saratov, Russia", 
          "id": "http://www.grid.ac/institutes/grid.78837.33", 
          "name": [
            "Yurii Gagarin State Technical University of Saratov, Saratov, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Krysko", 
        "givenName": "V. A.", 
        "id": "sg:person.015167266033.92", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015167266033.92"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "National Research Tomsk Polytechnic University, Tomsk, Russia", 
          "id": "http://www.grid.ac/institutes/grid.27736.37", 
          "name": [
            "Yurii Gagarin State Technical University of Saratov, Saratov, Russia", 
            "National Research Tomsk Polytechnic University, Tomsk, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Papkova", 
        "givenName": "I. V.", 
        "id": "sg:person.010261455615.35", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010261455615.35"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Yurii Gagarin State Technical University of Saratov, Saratov, Russia", 
          "id": "http://www.grid.ac/institutes/grid.78837.33", 
          "name": [
            "Yurii Gagarin State Technical University of Saratov, Saratov, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Zhigalov", 
        "givenName": "M. V.", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "National Research Tomsk Polytechnic University, Tomsk, Russia", 
          "id": "http://www.grid.ac/institutes/grid.27736.37", 
          "name": [
            "Yurii Gagarin State Technical University of Saratov, Saratov, Russia", 
            "National Research Tomsk Polytechnic University, Tomsk, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Krysko", 
        "givenName": "A. V.", 
        "id": "sg:person.016017316223.58", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016017316223.58"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2020-07-14", 
    "datePublishedReg": "2020-07-14", 
    "description": "In this paper, we construct a new theory of nanobeams taking into account the dependence of the material properties on the stress state. The theory is based on the Euler\u2013Bernoulli kinematic model in the first approximation. The beam material is isotropic but heterogeneous. For the first time, the physical nonlinearity and the dependence of the material properties on the temperature are taken into account in the study of nanobeams, and the theory is developed for arbitrary materials. It is based on the theory of small elasticplastic strains and on the the modified torque theory of elasticity. The stationary temperature field is determined by solving the three-dimensional Poisson equation with boundary conditions of orders 1\u20133. The initial equations are derived from the Hamilton\u2013Ostrogradskii principle. The desired system of partial differential equations is reduced to the Cauchy problem by the finite difference method of the second order of accuracy, and the Cauchy problem is solved by the Runge\u2013Kutta or Newmark method. At each time step, an iterative procedure is developed by the Birger method of variable elasticity parameters. The stationary solution follows from the dynamic solution of the problem obtained by the method of determination (the method of the parameter position). The convergence of the solution is investigated depending on the number of points of partition along the length and thickness of the beam in the finite difference method as well as on the method of solving the Cauchy problem and the size-dependent parameter, i.e., the solution of the problem is considered to have almost infinite number of degrees of freedom. Numerical examples are given for a beam rigidly clamped at the ends with the stress-strain diagram for aluminum. Accounting for the size-dependent parameter in the nanobeam theory significantly affects the load-carrying capacity of nanobeams.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s11182-020-02065-9", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1313824", 
        "issn": [
          "1064-8887", 
          "1573-9228"
        ], 
        "name": "Russian Physics Journal", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "63"
      }
    ], 
    "keywords": [
      "Cauchy problem", 
      "finite difference method", 
      "size-dependent parameters", 
      "nanobeam theory", 
      "difference method", 
      "partial differential equations", 
      "three-dimensional Poisson equation", 
      "Hamilton\u2013Ostrogradskii principle", 
      "physical nonlinearity", 
      "variable elasticity parameters", 
      "stationary temperature field", 
      "initial equations", 
      "differential equations", 
      "stationary solutions", 
      "Runge-Kutta", 
      "number of points", 
      "numerical examples", 
      "Poisson equation", 
      "torque theory", 
      "infinite number", 
      "second order", 
      "arbitrary materials", 
      "beam material", 
      "time step", 
      "Newmark method", 
      "iterative procedure", 
      "dynamic solution", 
      "nanobeams", 
      "boundary conditions", 
      "equations", 
      "order 1", 
      "first approximation", 
      "account physical nonlinearity", 
      "material properties", 
      "temperature field", 
      "elasticity parameters", 
      "theory", 
      "desired system", 
      "new theory", 
      "nonlinearity", 
      "kinematic model", 
      "problem", 
      "solution", 
      "beam", 
      "approximation", 
      "parameters", 
      "method of determination", 
      "convergence", 
      "dependence", 
      "properties", 
      "account", 
      "diagram", 
      "field", 
      "freedom", 
      "partition", 
      "number", 
      "accuracy", 
      "model", 
      "principles", 
      "elasticity", 
      "point", 
      "stress state", 
      "system", 
      "order", 
      "state", 
      "first time", 
      "temperature", 
      "step", 
      "conditions", 
      "procedure", 
      "thickness", 
      "load-carrying capacity", 
      "materials", 
      "length", 
      "stress-strain diagram", 
      "time", 
      "degree", 
      "determination", 
      "end", 
      "aluminum", 
      "study", 
      "capacity", 
      "strains", 
      "method", 
      "example", 
      "paper", 
      "Euler\u2013Bernoulli kinematic model", 
      "study of nanobeams", 
      "small elasticplastic strains", 
      "elasticplastic strains", 
      "modified torque theory", 
      "Birger method"
    ], 
    "name": "Nanobeam Theory Taking Into Account Physical Nonlinearity", 
    "pagination": "522-529", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1129355922"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11182-020-02065-9"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11182-020-02065-9", 
      "https://app.dimensions.ai/details/publication/pub.1129355922"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T19:00", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_863.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s11182-020-02065-9"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s11182-020-02065-9'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11182-020-02065-9'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11182-020-02065-9'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11182-020-02065-9'


 

This table displays all metadata directly associated to this object as RDF triples.

174 TRIPLES      21 PREDICATES      117 URIs      109 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11182-020-02065-9 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author N7062c0354f964b73a29d9ae82ed8ba36
4 schema:datePublished 2020-07-14
5 schema:datePublishedReg 2020-07-14
6 schema:description In this paper, we construct a new theory of nanobeams taking into account the dependence of the material properties on the stress state. The theory is based on the Euler–Bernoulli kinematic model in the first approximation. The beam material is isotropic but heterogeneous. For the first time, the physical nonlinearity and the dependence of the material properties on the temperature are taken into account in the study of nanobeams, and the theory is developed for arbitrary materials. It is based on the theory of small elasticplastic strains and on the the modified torque theory of elasticity. The stationary temperature field is determined by solving the three-dimensional Poisson equation with boundary conditions of orders 1–3. The initial equations are derived from the Hamilton–Ostrogradskii principle. The desired system of partial differential equations is reduced to the Cauchy problem by the finite difference method of the second order of accuracy, and the Cauchy problem is solved by the Runge–Kutta or Newmark method. At each time step, an iterative procedure is developed by the Birger method of variable elasticity parameters. The stationary solution follows from the dynamic solution of the problem obtained by the method of determination (the method of the parameter position). The convergence of the solution is investigated depending on the number of points of partition along the length and thickness of the beam in the finite difference method as well as on the method of solving the Cauchy problem and the size-dependent parameter, i.e., the solution of the problem is considered to have almost infinite number of degrees of freedom. Numerical examples are given for a beam rigidly clamped at the ends with the stress-strain diagram for aluminum. Accounting for the size-dependent parameter in the nanobeam theory significantly affects the load-carrying capacity of nanobeams.
7 schema:genre article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N3ca094d3fcdb47bc8d3b09229e5b84a3
11 Nac2186b102714805930892695b780b91
12 sg:journal.1313824
13 schema:keywords Birger method
14 Cauchy problem
15 Euler–Bernoulli kinematic model
16 Hamilton–Ostrogradskii principle
17 Newmark method
18 Poisson equation
19 Runge-Kutta
20 account
21 account physical nonlinearity
22 accuracy
23 aluminum
24 approximation
25 arbitrary materials
26 beam
27 beam material
28 boundary conditions
29 capacity
30 conditions
31 convergence
32 degree
33 dependence
34 desired system
35 determination
36 diagram
37 difference method
38 differential equations
39 dynamic solution
40 elasticity
41 elasticity parameters
42 elasticplastic strains
43 end
44 equations
45 example
46 field
47 finite difference method
48 first approximation
49 first time
50 freedom
51 infinite number
52 initial equations
53 iterative procedure
54 kinematic model
55 length
56 load-carrying capacity
57 material properties
58 materials
59 method
60 method of determination
61 model
62 modified torque theory
63 nanobeam theory
64 nanobeams
65 new theory
66 nonlinearity
67 number
68 number of points
69 numerical examples
70 order
71 order 1
72 paper
73 parameters
74 partial differential equations
75 partition
76 physical nonlinearity
77 point
78 principles
79 problem
80 procedure
81 properties
82 second order
83 size-dependent parameters
84 small elasticplastic strains
85 solution
86 state
87 stationary solutions
88 stationary temperature field
89 step
90 strains
91 stress state
92 stress-strain diagram
93 study
94 study of nanobeams
95 system
96 temperature
97 temperature field
98 theory
99 thickness
100 three-dimensional Poisson equation
101 time
102 time step
103 torque theory
104 variable elasticity parameters
105 schema:name Nanobeam Theory Taking Into Account Physical Nonlinearity
106 schema:pagination 522-529
107 schema:productId N1831a2b68f8f4a9b869428682690e17e
108 Nf4a220b300504d7c88dd03b42fc3247c
109 schema:sameAs https://app.dimensions.ai/details/publication/pub.1129355922
110 https://doi.org/10.1007/s11182-020-02065-9
111 schema:sdDatePublished 2022-01-01T19:00
112 schema:sdLicense https://scigraph.springernature.com/explorer/license/
113 schema:sdPublisher N6631de8833764900802bc6d5a4a57431
114 schema:url https://doi.org/10.1007/s11182-020-02065-9
115 sgo:license sg:explorer/license/
116 sgo:sdDataset articles
117 rdf:type schema:ScholarlyArticle
118 N1831a2b68f8f4a9b869428682690e17e schema:name doi
119 schema:value 10.1007/s11182-020-02065-9
120 rdf:type schema:PropertyValue
121 N3ca094d3fcdb47bc8d3b09229e5b84a3 schema:volumeNumber 63
122 rdf:type schema:PublicationVolume
123 N4417af8f30854656ad73e1634d27266f rdf:first sg:person.016017316223.58
124 rdf:rest rdf:nil
125 N4cb65f2863524274b8c0e4868271c106 rdf:first Na0c606f6de7f4c698e461af1d6f9cb25
126 rdf:rest N4417af8f30854656ad73e1634d27266f
127 N6631de8833764900802bc6d5a4a57431 schema:name Springer Nature - SN SciGraph project
128 rdf:type schema:Organization
129 N702a3eed503742259179b1241890eb8e rdf:first sg:person.010261455615.35
130 rdf:rest N4cb65f2863524274b8c0e4868271c106
131 N7062c0354f964b73a29d9ae82ed8ba36 rdf:first sg:person.015167266033.92
132 rdf:rest N702a3eed503742259179b1241890eb8e
133 Na0c606f6de7f4c698e461af1d6f9cb25 schema:affiliation grid-institutes:grid.78837.33
134 schema:familyName Zhigalov
135 schema:givenName M. V.
136 rdf:type schema:Person
137 Nac2186b102714805930892695b780b91 schema:issueNumber 3
138 rdf:type schema:PublicationIssue
139 Nf4a220b300504d7c88dd03b42fc3247c schema:name dimensions_id
140 schema:value pub.1129355922
141 rdf:type schema:PropertyValue
142 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
143 schema:name Mathematical Sciences
144 rdf:type schema:DefinedTerm
145 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
146 schema:name Numerical and Computational Mathematics
147 rdf:type schema:DefinedTerm
148 sg:journal.1313824 schema:issn 1064-8887
149 1573-9228
150 schema:name Russian Physics Journal
151 schema:publisher Springer Nature
152 rdf:type schema:Periodical
153 sg:person.010261455615.35 schema:affiliation grid-institutes:grid.27736.37
154 schema:familyName Papkova
155 schema:givenName I. V.
156 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010261455615.35
157 rdf:type schema:Person
158 sg:person.015167266033.92 schema:affiliation grid-institutes:grid.78837.33
159 schema:familyName Krysko
160 schema:givenName V. A.
161 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015167266033.92
162 rdf:type schema:Person
163 sg:person.016017316223.58 schema:affiliation grid-institutes:grid.27736.37
164 schema:familyName Krysko
165 schema:givenName A. V.
166 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016017316223.58
167 rdf:type schema:Person
168 grid-institutes:grid.27736.37 schema:alternateName National Research Tomsk Polytechnic University, Tomsk, Russia
169 schema:name National Research Tomsk Polytechnic University, Tomsk, Russia
170 Yurii Gagarin State Technical University of Saratov, Saratov, Russia
171 rdf:type schema:Organization
172 grid-institutes:grid.78837.33 schema:alternateName Yurii Gagarin State Technical University of Saratov, Saratov, Russia
173 schema:name Yurii Gagarin State Technical University of Saratov, Saratov, Russia
174 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...