### Browsing by Author "von Hertzen, Raimo"

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Item Bridging plate theories and elasticity solutions(PERGAMON-ELSEVIER SCIENCE LTD, 2017) Karttunen, Anssi; von Hertzen, Raimo; Reddy, JN; Romanoff, Jani; Department of Mechanical Engineering; Texas A&M UniversityIn this work, we present an exact 3D plate solution in the conventional form of 2D plate theories without invoking any of the assumptions inherent to 2D plate formulations. We start by formulating a rectangular plate problem by employing Saint Venant’s principle so that edge effects do not appear in the plate. Then the exact general 3D elasticity solution to the formulated interior problem is examined. By expressing the solution in terms of mid-surface variables, exact 2D equations are obtained for the rectangular interior plate. It is found that the 2D presentation includes the Kirchhoff, Mindlin and Levinson plate theories and their general solutions as special cases. The key feature of the formulated interior plate problem is that the interior stresses of the plate act as surface tractions on the lateral plate edges and contribute to the total potential energy of the plate. We carry out a variational interior formulation of the Levinson plate theory and take into account, as a novel contribution, the virtual work due to the interior stresses along the plate edges. Remarkably, this way the resulting equilibrium equations become the same as in the case of a vectorial formulation. A gap in the conventional energy-based derivations of 2D engineering plate theories founded on interior kinematics is that the edge work due to the interior stresses is not properly accounted for. This leads to artificial edge effects through higher-order stress resultants. Finally, a variety of numerical examples are presented using the 3D elasticity solution.Item Dynamic response of a cylinder cover under a moving load(2014) Karttunen, Anssi; von Hertzen, Raimo; Department of Applied MechanicsItem Exact elasticity-based finite element for circular plates(Elsevier Limited, 2017) Karttunen, Anssi; von Hertzen, Raimo; Reddy, Junthula; Romanoff, Jani; Department of Mechanical Engineering; Texas A&M UniversityIn this paper, a general elasticity solution for the axisymmetric bending of a linearly elastic annular plate is used to derive an exact finite element for such a plate. We start by formulating an interior plate problem by employing Saint Venant’s principle so that edge effects do not appear in the plate. Then the elasticity solution to the formulated interior problem is presented in terms of mid-surface variables so that it takes a form similar to conventional engineering plate theories. By using the mid-surface variables, the exact finite element is developed both by force- and energy-based approaches. The central, nonstandard feature of the interior solution, and the finite element based on it, is that the interior stresses of the plate act as surface tractions on the plate edges and contribute to the total potential energy of the plate. Finally, analytical and numerical examples are presented using the elasticity solution and the derived finite element.Item Exact theory for a linearly elastic interior beam(2016-01-01) Karttunen, Anssi T.; von Hertzen, Raimo; Department of Mechanical EngineeringIn this paper, an elasticity solution for a two-dimensional (2D) plane beam is derived and it is shown that the solution provides a complete framework for exact one-dimensional (1D) presentations of plane beams. First, an interior solution representing a general state of any 2D linearly elastic isotropic plane beam under a uniform distributed load is obtained by employing a stress function approach. The solution excludes the end effects of the beam and is valid sufficiently far away from the beam boundaries. Then, three kinematic variables defined at the central axis of the plane beam are formed from the 2D displacement field. Using these central axis variables, the 2D interior elasticity solution is presented in a novel manner in the form of a 1D beam theory. By applying the Clapeyron's theorem, it is shown that the stresses acting as surface tractions on the lateral end surfaces of the interior beam need to be taken into account in all energy-based considerations related to the interior beam. Finally, exact1D rod and beam finite elements are developed by the aid of the axis variables from the 2D solution. (C) 2015 Elsevier Ltd. All rights reserved.Item Identification of the viscoelastic parameters of a polymer model by the aid of a MCMC method(2014) Haario, Heikki; von Hertzen, Raimo; Karttunen, Anssi; Jorkama, Marko; Department of Applied MechanicsItem A numerical study of traveling waves in a viscoelastic cylinder cover under rolling contact(2013) Karttunen, Anssi; von Hertzen, Raimo; Department of Applied Mechanics; Department of Mechanical EngineeringItem Polymer cover induced self-excited vibrations of nipped rolls(Elsevier BV, 2011) Karttunen, Anssi T.; von Hertzen, Raimo; Konetekniikan laitos; Department of Mechanical Engineering; Insinööritieteiden korkeakoulu; School of EngineeringItem Shear deformable plate elements based on exact elasticity solution(Elsevier Limited, 2018-04-15) Karttunen, Anssi T.; von Hertzen, Raimo; Reddy, J. N.; Romanoff, Jani; Department of Mechanical Engineering; Texas A&M UniversityThe 2-D approximation functions based on a general exact 3-D plate solution are used to derive locking-free, rectangular, 4-node Mindlin (i.e., first-order plate theory), Levinson (i.e., a third-order plate theory), and Full Interior plate finite elements. The general plate solution is defined by a biharmonic mid-surface function, which is chosen for the thick plate elements to be the same polynomial as used in the formulation of the well-known nonconforming thin Kirchhoff plate element. The displacement approximation that stems from the biharmonic polynomial satisfies the static equilibrium equations of the 2-D plate theories at hand, the 3-D Navier equations of elasticity, and the Kirchhoff constraints. Weak form Galerkin method is used for the development of the finite element model, and the matrices for linear bending, buckling and dynamic analyses are obtained through analytical integration. In linear buckling problems, the 2-D Full Interior and Levinson plates perform particularly well when compared to 3-D elasticity solutions. Natural frequencies obtained suggest that the optimal value of the shear correction factor of the Mindlin plate theory depends primarily on the boundary conditions imposed on the transverse deflection of the 3-D plate used to calibrate the shear correction factor.Item Variational formulation of the static Levinson beam theory(2015-06) Karttunen, Anssi T.; von Hertzen, Raimo; Department of Mechanical EngineeringIn this communication, we provide a consistent variational formulation for the static Levinson beam theory. First, the beam equations according to the vectorial formulation by Levinson are reviewed briefly. By applying the Clapeyron's theorem, it is found that the stresses on the lateral end surfaces of the beam are an integral part of the theory. The variational formulation is carried out by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the stresses on the end surfaces of the beam. This external virtual work contributes to the boundary conditions in such a way that artificial end effects do not appear in the theory. The obtained beam equations are the same as the vectorially derived Levinson equations. Finally, the exact Levinson beam finite element is developed. (C) 2015 Elsevier Ltd. All rights reserved.