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Obliczenia numeryczne przekryć Pragera PDF Print E-mail
R. Czubacki, G. Dzierżanowski, T. Lewiński, Obliczenia numeryczne przekryć Pragera, Inżynieria i Budownictwo, 2021, nr 1-2, str 80-84
 
Third formulation of the space-time finite element method PDF Print E-mail
Z. Kacprzyk, Third formulation of the space-time finite element method, RSP 2020, IOP Conference Series: Materials Science and Engineering, Volume 1015, XXIX R-P-S Seminar 2020 November 2020, Wroclaw, Poland, DOI: 10.1088/1757-899x/1015/1/012005
 on-line>>

Abstract
The paper explains differences existing between the space-time finite elements, which fundamentals were presented by the Kączkowski in 1975 and 1976, and its modification. The replacement of load with concentrated forces and moments (which are to satisfy equilibrium conditions at nodes) was given up, namely in the latter one; instead, a requirement was made that functions approximating the solution would satisfy differential equation in inter-node areas in a specified integral way. This leads to a system of algebraic equations, in which kinematic parameters existing in the solution approximating functions are the unknowns. Displacements and their derivatives (of any order) at nodes are those parameters.
 
Optimum design of elastic moduli for the multiple load problems PDF Print E-mail
T. Lewiński, Optimum design of elastic moduli for the multiple load problems,  Archives of Mechanics vol. 73 (1), pp 27-66, 2021,
 DOI: 10.24423/aom.3607
https://am.ippt.pan.pl/am/article/view/3607

Abstract
The paper deals with minimization of the weighted average of compliances of structures, made of an elastic material of spatially varying elasticity moduli, subjected to n load variants acting non-simultaneously. The trace of the Hooke tensor is assumed as the unit cost of the design. Three versions of the free material design are discussed: designing the moduli of arbitrary anisotropy (AMD), designing the moduli of an isotropic material (IMD), designing of Young’s modulus for a fixed Poisson ratio (YMD). The problem is in all cases reduced to the Linear Constrained Problem (LCP) of Bouchitté and Fragalà consisting of two mutually dual problems: stress based and strain based, the former one being characterized by the integrand of linear growth depending on the trial statically admissible stresses. The paper shows equivalence of the stress fields solving the (LCP) problem and those appearing in the optimal body subjected to subsequent load cases.

 
Analysis of a reinforced concrete dome PDF Print E-mail
P. Czumaj, S. Dudziak and Z. Kacprzyk, Analysis of a reinforced concrete dome, RSP 2020, IOP Conference Series: Materials Science and Engineering, Volume 1015, XXIX R-P-S Seminar 2020 November 2020, Wroclaw, Poland, DOI: 10.1088/1757-899x/1015/1/012006
on-line>>

Abstract
FEM models of axi-symmetrical reinforced concrete dome with two rings have been analysed. Different complexity level of computational models (2D and 3D), geometry simplifications and FEM codes (Abaqus, FEAS, ARSAP) have been compared. Assessment of building structure deflections has been performed with several approaches, which gave opportunity to confront them and estimate mistakes of most commonly used models.
 
On incorporating warping effects due to transverse shear and torsion into the theories of straight elastic bars PDF Print E-mail
T. Lewiński, S.Czarnecki, On incorporating warping effects due to transverse shear and torsion into the theories of straight elastic bars, Acta Mech (2020).

https://doi.org/10.1007/s00707-020-02849-7

Abstract
By endowing El Fatmi’s theories of bars with first-order warping functions due to torsion and shear, a family of theories of bars, of various applicability ranges, is effectively constructed. The theories thus formed concern bars of arbitrary cross-sections; they are reformulations of the mentioned theories by El Fatmi and theories by Kim and Kim, Librescu and Song, Vlasov and Timoshenko. The Vlasov-like theory thus developed is capable of describing the torsional buckling and lateral buckling phenomena of bars of both solid and thin-walled cross-sections, which reflects the non-trivial correspondence, noted by Wagner and Gruttmann, between the torsional St.Venant’s warping function and the contour-wise defined warping functions proposed by Vlasov. Moreover, the present paper delivers an explicit construction of the constitutive equations of Timoshenko’s theory; the equations linking transverse forces with the measures of transverse shear turn out to be coupled for all bars of asymmetric cross-sections. The modeling is hierarchical: the warping functions are numerically constructed by solving the three underlying 2D scalar elliptic problems, providing the effective characteristics for the 1D models of bars. The 2D and 1D problems are indissolubly bonded, thus forming a unified scientific tool, deeply rooted in the hitherto existing knowledge on elasticity of elastic straight bars.
 
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