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1

Searching for optimal prestressing of steel bar structures based on sensitivity analysis

Yurchenko V. V., Peleshko I. D.

Archives of Civil Engineering

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2020

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Vol. 66, nr 3

525--540

EN

The paper considers parametric optimization problems for the steel bar structures formulated as nonlinear programming ones with variable unknown cross-sectional sizes of the structural members, as well as initial prestressing forces introduced into the specified redundant members of the structure. The system of constraints covers load-bearing capacity constraints for all the design sections of the structural members subjected to all the design load combinations at ultimate limit state, as well as displacement constraints for the specified nodes of the bar system, subjected to all design load combinations at serviceability limit state. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimization problem. A numerical technique to determine the optimal number of the redundant members to introduce the initial prestressing forces has been offered for high-order statically indeterminate bar structures. It reduces the dimension for the design variable vector of unknown initial prestressing forces for considered optimization problems.

2

Metoda rzutowania gradientu w optymalizacji parametrów konstrukcyjnych napięciowego transformatora pomiarowego

Piaskowy A., Roj J.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 1a

91--93

PL

W pracy sformułowano problem optymalizacji parametrów konstrukcyjnych precyzyjnych transformatorów pomiarowych. Zaproponowano metodę optymalizacji bazującą na rzutowaniu gradientu na podprzestrzeń styczną do ograniczeń aktywnych oraz przedstawiono algorytm.

EN

The design optimization problem of precise measuring transformers is formulated in the paper. Gradient projection on active tangent subspace method is proposed for the task solutions and algorithm is shown.

3

Approximate gradient projection method with general Runge-Kutta schemes and piecewise polynomial controls for optimal control problems

Chryssoverghi I.

Control and Cybernetics

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2005

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Vol. 34, no 2

425-451

EN

This paper addresses the numerical solution of optimal control problems for systems described by ordinary differential equations with control constraints. The state equation is discretized by a general explicit Runge-Kutta scheme and the controls are approximated by functions that are piecewise polynomial, but not necessarily continuous. We then propose an approximate gradient projection method that constructs sequences of discrete controls and progressively refines the discretization. Instead of using the exact discrete cost derivative, which usually requires tedious calculations, we use here an approximate derivative of the cost functional denned by discretizing the continuous adjoint equation by the same Runge-Kutta scheme backward and the integral involved by a Newton-Cotes integration rule, both involving maximal order intermediate approximations. The main result is that strong accumulation points in L2, if they exist, of sequences generated by this method satisfy the weak necessary conditions for optimality for the continuous problem. In the unconstrained case and under additional assumptions, we prove strong convergence in L2 and derive an a posteriori error estimate. Finally, numerical examples are given.