NI Xiao-qin, CHENG Geng-dong. Optimal Design of Thin Solid Elastic Plates Under Thermal Load[J]. Applied Mathematics and Mechanics, 2015, 36(3): 233-241. doi: 10.3879/j.issn.1000-0887.2015.03.001
Citation: NI Xiao-qin, CHENG Geng-dong. Optimal Design of Thin Solid Elastic Plates Under Thermal Load[J]. Applied Mathematics and Mechanics, 2015, 36(3): 233-241. doi: 10.3879/j.issn.1000-0887.2015.03.001

Optimal Design of Thin Solid Elastic Plates Under Thermal Load

doi: 10.3879/j.issn.1000-0887.2015.03.001
  • Received Date: 2014-11-11
  • Rev Recd Date: 2015-01-07
  • Publish Date: 2015-03-15
  • Plates and shells constitute a large family of widely used structural elements. Under the action of thermal load, if the thermal expansion is restricted, membrane forces and bending moments will occur within the plate and shell structures and lead to large deformation which seriously affected normal service. Due to the particularity of thermal load, uniform increase of the plate or shell thickness can hardly reduce the thermal deformation and thermal stress effectively, and special experience and knowledge are required in thermal structural design. Thickness distribution optimization of the thin elastic plate structure with given material volume under thermal load was studied and aimed at reduction of thermal deformation. For the thickness distribution of the plate with given material volume, mathematical formulation of the optimization problem focused on minimum structural deformation energy was established. According to the formulation and with the variational method, the optimality criteria and the iterative scheme for modification of the thickness distribution were derived. And this optimization algorithm was implemented through secondary development in the commercial finite element programs. Results of the numerical examples show that, the presented method greatly reduces the thermal deformation of thin elastic plate structures through modification of the thickness distribution, and makes an effective optimization method for thermal structures.
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