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EN
In the article, the pure bending problem for strip (beam) with straight, perpendicular to its axis crack located in the zone of tensile stresses is investigated on the assumption of narrow plastic strips near crack tips. Using methods of the theory of functions of a complex variable and complex potentials, the problem is reduced to the several linear conjunction problems. The solutions of latter problems are ob-tained in the class of functions confined in the edges of plastic strips. Formulas for the calculation of their lengths are derived. Expressions for the determination of crack tip opening values are written. Numerical analysis of the problem is performed.
EN
The subject of the paper are cold-formed, thin-walled non-standard channel beams with stiffened webs. The local elastic buckling and limit load of the beams subjected topure bending are investigated. This study includes numerical, based on the Finite Element Method and the Finite Strip Method, calculations and actual tests of beams in the laboratory. The presented results give a deep insight into behaviour of such beams and may be used to validate analytical models.
EN
The main objective of this work is the numerical analysis (FE analysis) of stability of three-layer beams with metal foam core (alumina foam core). The beams were subjected to pure bending. The analysis of the local buckling was performed. Furthermore, the influence of geometric parameters of the beam and material properties of the core (linear and non-linear model) on critical loads values and buckling shape were also investigated. The calculations were made on a family of beams with different mechanical properties of the core (elastic and elastic-plastic material). In addition, the influence of geometric imperfections on deflection and normal stress values of the core and the faces has been evaluated.
PL
Przedmiotem pracy są belki trójwarstwowe poddane czystemu zginaniu. Opisano i rozwiązano problem wyboczenia-zmarszczenia okładziny ściskanej. Równanie równowagi wyznaczono z zasady stacjonarności całkowitej energii potencjalnej, którego całką są funkcje hiperboliczne. Badania numeryczne przeprowadzono dla rodziny belek o różnych właściwościach mechanicznych rdzenia. Ponadto przeprowadzono badania numeryczne MES. Obciążenia krytyczne otrzymane z obu metod zestawiono w tabelach i na wykresach.
EN
The subject of the paper are sandwich beams under pure bending. The problem of buckling-wrinkling of a compression face is described and solved. The equation of equilibrium is obtained based on the principle of stationary total potential energy. The analytical solution of this equation is composed of hyperbolic functions. Numerical calculations are realized for a family of sandwich beams with different mechanical properties of the core. Moreover, FEM investigations are realized. Results of both methods are compared and presented in tables and figures.
5
Content available remote Large bending deformations of pressurized curved tubes
EN
In this paper, the problem of large pure bending deformations of membrane is considered. The membrane is a sector of torus with a closed cross-section. This membrane is called a curved tube for short. We consider the homogenous, incompressible, isotropic and hyperelastic material. The external load is a constant pressure and bending couples acting at the edges. The equilibrium equations reduce to ordinary differential equations. As an example, the membrane with a constant thickness and with a circular cross-section is investigated.
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