Instability of optimal equilibria in the minimum mass design of uniform shallow arches
DOI10.1007/BF00935226zbMath0501.73091MaRDI QIDQ1172449
Publication date: 1983
Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)
local minimumnecessary and sufficient conditionsnonlinear optimal controlexampleunstableoptimal equilibriumminimum mass designfixed spanarbitrarily loaded uniform shallow archescritical point conditiondifferential equations of axial and transverse equilibrium of arch as side conditionsinitial curvature and axial load as design variablesmass as criterionnonunique with one equilibrium unstable and other stable after snap-throughsinusoidally loaded hinged-hinged archstability of equilibria becomes integral part of solutionstable after snap-through
Optimality conditions for problems involving partial differential equations (49K20) Bifurcation and buckling (74G60) Membranes (74K15) Optimization problems in solid mechanics (74P99)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The calculus of variations and optimal control. An introduction
- On a variational problem with unknown boundaries and the determination of optimal shapes of elastic bodies
- Uniform shallow arches of minimum weight and minimum maximum deflection
- A sufficiency theorem for optimal control
- STABILITY OF THE NATURAL SHAPES OF SINUSOIDALLY LOADED UNIFORM SHALLOW ARCHES
- Natural Structural Shapes of Shallow Arches
- NATURAL STRUCTURAL SHAPES (THE STATIC CASE)
- The Strongest Circular Arch—A Perturbation Solution
This page was built for publication: Instability of optimal equilibria in the minimum mass design of uniform shallow arches
