By H. E. Rauch

ISBN-10: 0080305741

ISBN-13: 9780080305745

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Read or Download Applications of Nonlinear Programming to Optimization and Control. Proceedings of the 4th IFAC Workshop, San Francisco, USA, 20–21 June 1983 PDF

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Additional info for Applications of Nonlinear Programming to Optimization and Control. Proceedings of the 4th IFAC Workshop, San Francisco, USA, 20–21 June 1983

Example text

I+l,3 13 13 Associate with each pair (i,j) the point P.. ). By labeling each triangle ij J 13 with its^three vertices the "triangularization of Ω. is h τ, = {(P. ,P. ,P. g + l5 · 1 < i < N-1, 1 5 j < M-l}. IS The finite element approximation is vv = { w c 0 ( V' (40) φ, is linear on each triangle in τ μ } . The dimension of W. (Ω. ) i s K=MxN and an e l e ­ ft n ment φ, of W, (S, ) i s completely s p e c i f i e d by the K-vector φ = {φ Jl 5 I < K}, φ , . 1 W . = φ, ψ Ύ κ(r. / £ . ) , 1 5 Jj 5 M, 1 < i < N.

Finite element method; INTRODUCTION thermal radiator; Any other surfaces of the radiator may be treated as adiabatic. Two constraints res­ trict freedom in the design of the thermal radiator: (i) The maximum temperature at the box/ radiator interface is not to exceed some constant (typ. 50°C), and (ii) no part of the radiator is to be thin­ ner than some constant (typ. 1 mm). Current trends indicate that future communi­ cations satellites and spacecrafts will grow ever larger, consume ever more electrical power and dissipate larger amounts of therm­ al energy.

Uniform inward thermal power flux at the contact surface (typ. 67X10-8 W / m 2 ^ ) e = surface emissivity (typ. 01 W/cm 2 ). The optimal design problem consists in mini­ mizing the volume J(R,L) = rr/J R(z)2dz (8) over a l l lengths L > 0 and shape functions R subject to the constraint T(x,y,z) 5 T £ (typ. 50°C) (9) V (x,y,z) € Σ ι β In the present analysis we drop the require­ ment (ii) in the introduction. / It is convenient to introduce the following changes of variables: * - r · ξ ι = k'ξ2 = k -λ = k (10) y « l , « 2 .

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Applications of Nonlinear Programming to Optimization and Control. Proceedings of the 4th IFAC Workshop, San Francisco, USA, 20–21 June 1983 by H. E. Rauch

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