Department of Structural Mechanics and Computer Aided Engineering
Sandwich plates of minimal compliance PDF Print E-mail
scz-tl-2008-mSandwich plates of minimal compliance, S. Czarnecki, M. Kursa, T. Lewiński,
Comput. Methods Appl. Mech. Engrg. 197 (2008) 4866–4881
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The subject of the paper is an optimal choice of material parameters characterizing the core layer of sandwichplates within the framework of the conventional plate theory in which the core layer is treated as soft in the in-plane direction. The mathematical description is similar to the Hencky–Reissner model of plates with transverse shear deformation. Here, however, the bending stiffnesses and the transverse shear stiffnesses can be designed independently. The present paper deals only with optimal design of the core layer to make the plate compliance minimal. Two core materials are at our disposal, which leads to the ill-posed problem. To consider it one should relax this problem by admitting composite domains and characterize their overall properties by the homogenization formulae. The numerical approach is based on this relaxed formulation thus making it mesh-independent. The equilibrium problem is solved by the DSG3 finite element method. The optimization results are found with using the convergent updating schemes of the COC method.
Michell structures formed on surfaces of revolution PDF Print E-mail
tl-2004-mMichell structures formed on surfaces of revolution, T. Lewiński,
Structural and Multidisciplinary Optimization 28, 20–30 (2004)
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The paper formulates the Michell-like problems for surface gridworks. Particular attention is devoted to the problem of designing the lightest fully stressed gridworks formed on surfaces of revolution. In the examples considered, the gridworks are subjected to torsion. Proof is given that the circular meridian is a minimizer of the weight (or volume) functional of a shell subjected to torsion, thus justifying the original Michell conjecture according to which just the spherical twisting shell is the lightest. The proof is based on the methods of the classical variational calculus and thus can be viewed as elementary. This result is confirmed by a direct comparison of the exact formulae for the weight of a spherical Michell shell with the exact formulae for the weights of optimal conical and cylindrical shells with the same fixed boundaries.
On refined plate models based on kinematical assumptions PDF Print E-mail
On refined plate models based on kinematical assumptions, T. Lewiński, Warsaw
Archive of Applied Mechanics, Volume 57, Number 2, 133-146 (1987)
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In the first part of the paper an energy-consistent model for thick, elastic, isotropic plates based upon Jemielita's kinematical hypothesis is proposed. Since no assumptions on stresses are stipulated the model is free of the usual discrepancy between stress and displacement fields, viz. no one of the constitutive equations being violated. The objective of the second part of the paper is to perform a passage from the model obtained to the simplified one which is energy-inconsistent. This latter model proves far-reaching similarities to the first Reissner theory and, on the other hand, when an appropriate change of the function standing for the averaged plate deflection is made, — to the Kelkel's considerations.
O stosowaniu funkcji wagowych w metodzie czasoprzestrzennych elementów skończonych PDF Print E-mail

O stosowaniu funkcji wagowych w metodzie czasoprzestrzennych elementów skończonych, Zbigniew Kacprzyk
Prace Naukowe Politechniki Warszawskiej, seria Budownictwo, z. 85, s. 83-95, 1984
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W pracy wyprowadzono pewną metodę numerycznego całkowania równania ruchu. Metoda sformułowana jest tylko w przemieszczeniach. W zależności od przyjetych parametrów otrzymujemy schemat całkowania jawny lub niejawny. Metoda jest w zasadzie uogólnieniem metody czasoprzestrzennych elementów skończonych. Podano kryterium statecznosci metody. Metoda w zależnosci od przyjętych współczynników może być warunkowo lub bezwarunkowo stabilna. Oceniono dokładność rozwiązania i podano algorytm metody. Porównano prezentowaną metodę z metodą Newmarka.
słowa kluczowe: numeryczne całkowanie równań ruchu, metoda czasoprzestrzennych elementów skończonych

On aplication of weighted functions in the space-time finite elements method
A new method of integration of equation of motion, formulated in dispalcements, is presented in the paper. Depending on adopted parameters an explicit or an implicit scheme is obtained. Close relationship is indicated to the space-time finite element method. Stability criterion is given. The method can be conditionally or unconditionally stable, depending on the adopted coefficients. A check on accuracy of the results is made and the algoritm of the method is presented. A comparision is made between the presented method and Newmark's method.
key words: numericat integration of equation of motion, space-time finite elements method

Comparison of some numerical integration methods for the equations of motion of systems with a finite number of degrees of freedom PDF Print E-mail

Comparison of some numerical integration methods for the equations of motion of systems with a finite number of degrees of freedom, Z.Kacprzyk, T.Lewiński
Engineering Transactions, 31, 2, pp. 213-240, 1983
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The subject of this paper are the numerical integration methods of the differential equations of vibration (in matrix form) of a physical system with a finite number of degress of freedom. Comparison was made between finite difference method, Newmark's method and Space-Time Finite Element method. The compared methods have been brought to a unified form, disclosing far-reaching similarities concerning the calculation methods of displacement and velocity. Analogies have been found between the recurrence formulae relating the displacement and velocity vectors in different methods. It was proved that these analogies allow for a comparative analysis of convergence of the three methods and confine it to the analysis of approximation of initial conditions and of external loads. Thirteen methods of approximation of initial conditions are discussed. New formulation is given of the Space-Time Finite Elements. The comparative analysis of convergence is limited to free oscillation of a system with a single degree od freedom.

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