Optimal design of fibre reinforced membrane structures

被引：0
作者：
Anders Klarbring
Bo Torstenfelt
Peter Hansbo
Mats G. Larson
机构：
[1] Linköping University,Division of Solid Mechanics
[2] Jönköping University,Department of Mechanical Engineering
[3] Umeå University,Department of Mathematics and Mathematical Statistics
来源：
Structural and Multidisciplinary Optimization | 2017年 / 56卷
关键词：
Membrane; Fiber reinforcement; Design optimization;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A design problem of finding an optimally stiff membrane structure by selecting one–dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic orthotropic model by appropriate assumptions. The design problem is given in the form of two minimization statements. After finite element discretization, the separate treatment of each of the two statements follows from classical results and methods of structural optimization: the stiffest orientation of reinforcing fibers coincides with principal stresses and the separate selection of density of fibers is a convex problem that can be solved by optimality criteria iterations. Numerical solutions are shown for two particular configurations. The first for a statically determined structure and the second for a statically undetermined one. The latter shows related but non-unique solutions.
引用
收藏
页码：781 / 789
页数：8
相关论文
共 28 条
[1]  
Barlow J(1976)Optimal stress locations in finite element models Int J Numer Methods Eng 10 243-251
[2]  
Beck A(2013)On the convergence of block coordinate descent type methods SIAM J Optim 23 2037-2060
[3]  
Tetruashvili AL(1975)A continum theory of elastic material surfaces Arch Rat Mech Anal 57 292-323
[4]  
Gurtin ME(1999)Optimal laminate design subject to single membrane loads Struct Optim 17 65-73
[5]  
Murdoch AI(1997)Parametrization in laminate design for optimal compliance Int J Solids Struct 34 415-434
[6]  
Hammer VB(2014)Finite element modeling of a linear mambrane shell problem using tangential differential calculus Comput Methods Appl Mech Eng 270 1-14
[7]  
Hammer VB(2015)Tangential differential calculus and the finite element modeling of a large deformation elastic membrane problem Comput Mech 56 87-95
[8]  
Bendsoe MP(2008)On the elastic moduli and compliances of transverely isotropic and orthotropic materials J Mech Mater Struct 3 153-171
[9]  
Lipton R(1994)The equations of Reissner-Mindlin plates obtained by the method of internal constraints Meccanica 29 143-157
[10]  
Pedersen P(2015)On the computation of the Hashin-Shtrikman bounds for transversely isotropic two-phase linear elastic fibre-reinforced composites J Eng Math 95 295-232
123