Volume 26, Issue 2
Implementation of Some Methods of Shape Design for Variational Inequalities

Rizwan Butt

J. Part. Diff. Eq., 26 (2013), pp. 122-137.

Published online: 2013-06

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  • Abstract

In this paper we present some results concerning the optimal shape design problem governed by the fourth-order variational inequalities. The problem can be considered as a model example for the design of the shapes for elastic-plastic problem. The computations are done by finite element method, and the performance criterion is minimized by the material derivative method. We also discuss the error estimates in the appropriate norm and present some numerical results. An example is used to clearly illustrate the essential elements of shape design problems.

  • Keywords

Sobolev space convexity optimal shape design variational inequalities approximation optimization techniques finite element method material derivative method

  • AMS Subject Headings

35-XX, 35Bxx, 35Qxx

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

fouzanbutt@yahoo.com (Rizwan Butt)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-26-122, author = {Butt , Rizwan}, title = {Implementation of Some Methods of Shape Design for Variational Inequalities}, journal = {Journal of Partial Differential Equations}, year = {2013}, volume = {26}, number = {2}, pages = {122--137}, abstract = {

In this paper we present some results concerning the optimal shape design problem governed by the fourth-order variational inequalities. The problem can be considered as a model example for the design of the shapes for elastic-plastic problem. The computations are done by finite element method, and the performance criterion is minimized by the material derivative method. We also discuss the error estimates in the appropriate norm and present some numerical results. An example is used to clearly illustrate the essential elements of shape design problems.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v26.n2.3}, url = {http://global-sci.org/intro/article_detail/jpde/5157.html} }
TY - JOUR T1 - Implementation of Some Methods of Shape Design for Variational Inequalities AU - Butt , Rizwan JO - Journal of Partial Differential Equations VL - 2 SP - 122 EP - 137 PY - 2013 DA - 2013/06 SN - 26 DO - http://doi.org/10.4208/jpde.v26.n2.3 UR - https://global-sci.org/intro/article_detail/jpde/5157.html KW - Sobolev space KW - convexity KW - optimal shape design KW - variational inequalities KW - approximation KW - optimization techniques KW - finite element method KW - material derivative method AB -

In this paper we present some results concerning the optimal shape design problem governed by the fourth-order variational inequalities. The problem can be considered as a model example for the design of the shapes for elastic-plastic problem. The computations are done by finite element method, and the performance criterion is minimized by the material derivative method. We also discuss the error estimates in the appropriate norm and present some numerical results. An example is used to clearly illustrate the essential elements of shape design problems.

Rizwan Butt. (2019). Implementation of Some Methods of Shape Design for Variational Inequalities. Journal of Partial Differential Equations. 26 (2). 122-137. doi:10.4208/jpde.v26.n2.3
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