### Browsing by Author "Karttunen, Anssi T."

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Item Closed-form solution for circular microstructure-dependent Mindlin plates(SPRINGER WIEN, 2017) Karttunen, Anssi T.; Reddy, J. N.; Romanoff, Jani; Department of Mechanical Engineering; Texas A&M UniversityIn this paper, we derive a general closed-form solution for the static, axisymmetric bending of solid and annular microstructure-dependent Mindlin plates based on the modified couple-stress theory. The solution is developed by employing a suitable change in displacement variables. The couple-stress solution contains modified Bessel functions which do not appear in the classical case. The stress distributions of the annular microstructure-dependent plate are obtained in terms of load resultants by using the general closed-form solution. Analytical and numerical examples considering solid and annular circular plates are presented. The examples include simply supported and clamped solid and annular plates subjected to a uniformly distributed load and annular plates attached to a point-loaded rigid shaft.Item Exact microstructure-dependent Timoshenko beam element(2016-06-01) Karttunen, Anssi T.; Romanoff, Jani; Reddy, J. N.; Department of Mechanical EngineeringIn this study, we develop an exact microstructure-dependent Timoshenko beam finite element. First, a Timoshenko beam model based on the modified couple-stress theory is reviewed briefly. The general closed-form solution to the equilibrium equations of the beam is derived. The two-dimensional in-plane stress distributions along the beam in terms of load resultants are obtained. In addition, the general solution can be used to model any distributed load which can be expressed as a Maclaurin series. Then, the solution is presented in terms of discrete finite element (FE) degrees of freedom. This representation yields the exact shape functions for the beam element. Finally, the exact beam finite element equations are obtained by writing the generalized forces at the beam ends using the FE degrees of freedom. Three calculation examples which have applications in micron systems and sandwich structures are presented.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 Hierarchy of beam models for lattice core sandwich structures(PERGAMON-ELSEVIER SCIENCE LTD, 2020-11) Karttunen, Anssi T.; Reddy, J. N.; Marine Technology; Texas A&M University; Department of Mechanical EngineeringA discrete-to-continuum transformation to model 2-D discrete lattices as energetically equivalent 1-D continuum beams is developed. The study is initiated in a classical setting but results in a non-classical two-scale micropolar beam model via a novel link within a unit cell between the second-order macrorotation-gradient and the micropolar antisymmetric shear deformation. The shear deformable micropolar beam is reduced to a couple-stress and two classical lattice beam models by successive approximations. The stiffness parameters for all models are given by the micropolar constitutive matrix. The four models are compared by studying stretching- and bending-dominated lattice core sandwich beams under various loads and boundary conditions. A classical 4th-order Timoshenko beam is an apt first choice for stretching-dominated beams, whereas the 6th-order micropolar model works for bending-dominated beams as well. The 6th-order couple-stress beam is often too stiff near point loads and boundaries. It is shown that the 1-D micropolar model leads to the exact 2-D lattice response in the absence of boundary effects even when the length of the 1-D beam (macrostructure) equals that of the 2-D unit cell (microstructure), that is, when L=l.Item Interior formulation of axisymmetric Levinson plate theory(2016-06-01) Karttunen, Anssi T.; Von Hertzen, Raimo; Department of Mechanical EngineeringIn this study, we show that the axisymmetric Levinson plate theory is exclusively an interior theory and we provide a consistent variational formulation for it. First, we discuss an annular Levinson plate according to a vectorial formulation. The boundary layer of the plate is not modeled and, thus, the interior stresses acting as surface tractions do work on the lateral edges of the plate. This feature is confirmed energetically by the Clapeyron's theorem. The variational formulation is carried out for the annular Levinson plate by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the tractions based on the interior stresses on the inner and outer lateral edges of the Levinson plate. The obtained plate equations are consistent with the vectorially derived Levinson equations. Finally, we develop an exact plate finite element both by a force-based method and from the total potential energy of the Levinson plate.Item Micropolar modeling approach for periodic sandwich beams(ELSEVIER SCI LTD, 2018-02-01) Karttunen, Anssi T.; Reddy, J. N.; Romanoff, Jani; Department of Mechanical Engineering; Marine TechnologyA micropolar Timoshenko beam formulation is developed and used to model web-core sandwich beams. The beam theory is derived by a vector approach and the general solution to the governing sixth-order equations is given. A nodally-exact micropolar Timoshenko beam finite element is derived using the solution. Bending and shear stiffness coefficients for a web-core sandwich beam are determined through unit cell analysis, where the split of the shear forces into symmetric and antisymmetric parts plays a pivotal role. Static bending of web-core beams is studied using the micropolar model as well as modified couple-stress and classical Timoshenko beam models. The micropolar 1-D results are in best agreement with 2-D web-core beam frame results. This is because the micropolar beam allows antisymmetric shear deformation to emerge at locations where the 2-D web-core deformations cannot be reduced to 1-D by considering only symmetric shear behavior.Item Nonlinear finite element analysis of lattice core sandwich beams(ELSEVIER SCIENCE BV, 2019-03-01) Nampally, Praneeth; Karttunen, Anssi T.; Reddy, J. N.; Texas A&M University; Marine Technology; Department of Mechanical EngineeringA geometrically nonlinear finite element model is developed for the bending analysis of micropolar Timoshenko beams using the principle of virtual displacements and linear Lagrange interpolation functions. The nonlinearity enters the model via a nonlinear von Kármán strain term that allows the micropolar beam to undergo moderate rotations. The nonlinear micropolar Timoshenko beam is used as an equivalent single layer model to study four different lattice core sandwich beams. A two-scale energy method is used to derive the micropolar constitutive equations for web, hexagonal, Y-frame and corrugated core topologies. Various bending cases are studied numerically using the developed 1-D finite element model. Reduced integration techniques are used to overcome the shear and membrane locking. The present 1-D results are in good agreement with the corresponding 2-D finite element beam frame results for global bending.Item Nonlinear finite element analysis of lattice core sandwich plates(Elsevier Limited, 2020-05) Nampally, Praneeth; Karttunen, Anssi T.; Reddy, J. N.; Department of Mechanical Engineering; Marine Technology; Texas A&M UniversityA displacement-based, geometrically nonlinear finite element model is developed for lattice core sandwich panels modeled as 2-D equivalent single-layer (ESL), first-order shear deformation theory (FSDT) micropolar plates. The nonlinearity is due to the moderate macrorotations of the plate which are modeled by including the von Karman nonlinear strains in the micropolar strain measures. Weak-form Galerkin formulation with linear Lagrange interpolations is used to develop the displacement finite element model. Selective reduced integration is used to eliminate shear locking and membrane locking. The novel finite element model is used to study the nonlinear bending and linear free vibrations of web-core and pyramid core sandwich panels. Clamped and free edge boundary conditions are considered for the first time for the 2-D micropolar ESL-FSDT plate theory. The present 2-D finite element results are in good agreement with the corresponding detailed 3-D FE results for the lattice core sandwich panels. The 2-D element provides computationally cost-effective solutions; in a nonlinear bending example, the number of elements required for the 2-D micropolar plate is of the order 10(3) , whereas for the corresponding 3-D model the order is 10(5) .Item On the foundations of anisotropic interior beam theories(2016-02-15) Karttunen, Anssi T.; Von Hertzen, Raimo; Department of Mechanical Engineering; Marine Technology; Solid MechanicsThis study has two main objectives. First, we use the Airy stress function to derive an exact general interior solution for an anisotropic two-dimensional (2D) plane beam. Second, we cast the solution into the conventional form of 1D beam theories to clarify some basic concepts related to anisotropic interior beams. The derived general solution provides the exact third-order interior kinematic description for the plane beam and includes the Levinson/Reddy-kinematics as a special case. By applying the Clapeyron's theorem, we show 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 in order to avoid artificial end effects. Exact 1D interior beam equations are formed from the general 2D solution. Finally, we develop an exact interior beam finite element based on the general solution. With full anisotropic coupling, the stiffness matrix of the element becomes initially asymmetric due to the interior nature of the plane beam. By redefining the generalized nodal axial forces of the element, the stiffness matrix takes a symmetric form.Item 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 A review on non-classical continuum mechanics with applications in marine engineering(TAYLOR & FRANCIS, 2020-07-01) Romanoff, Jani; Karttunen, Anssi T.; Varsta, Petri; Remes, Heikki; Reinaldo Goncalves, Bruno; Department of Mechanical EngineeringMarine structures are advanced material and structural assemblies that span over different length scales. The classical structural design approach is to separate these length scales. The used structural models are based on classical continuum mechanics. There are multiple situations where the classical theory breaks down. Non-classical effects tend arise when the size of the smallest repeating unit of a periodic structure is of the same order as the full structure itself. The aim of the present paper is to discuss representative problems from different length scales of ship structural design.Item 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 Steady-state vibration of a viscoelastic cylinder cover subjected to moving loads(2016-07-01) Karttunen, Anssi T.; Von Hertzen, Raimo; Department of Mechanical EngineeringThe dynamic steady-state response of a viscoelastic cylinder cover subjected to circumferentially moving constant point and distributed loads is studied using a 1D Pasternak-type foundation model. The cover material is modeled according to the generalized Maxwell model as an incompressible frequency-dependent viscoelastic material spanning a wide relaxation spectrum. The vibration response of the cover for a moving twin point load is obtained using a modal expansion approach. On the basis of the solution, additional moving load cases are derived. In the case of a single moving point load, representing a load resultant due to rolling contact, numerical calculations show that regardless of the viscoelastic damping in the model, the critical load speed for the system can be well estimated by a resonance condition. In the vicinity of the critical speed, an incipient traveling wave arises behind the moving load. The viscoelastic cover stiffens for increasing excitation frequencies, thus, the cover response dividesinto two separate mode branches, of which the low-mode branch is dominant. A method to suppress the traveling wave vibrations in the cover at supercritical speeds using a moving twin point load, adjusted according to a dominant resonating mode, is presented. Using a distributed moving load, it is shown that depending on the wavelength, a traveling wave generated at the leading edge of the load may be reinforced at the trailing edge, the lift-off point, of the load. The developed model offers a fast and reliable way for practitioners to estimate the critical speeds of rolling contact machines with viscoelastic covers.Item Two-scale constitutive modeling of a lattice core sandwich beam(Elsevier Limited, 2019-03-01) Karttunen, Anssi T.; Reddy, J. N.; Romanoff, Jani; Department of Mechanical Engineering; Marine Technology; Texas A&M UniversityConstitutive equations are derived for a 1-D micropolar Timoshenko beam made of a web-core lattice material. First, a web-core unit cell is modeled by discrete classical constituents, i.e., the Euler–Bernoulli beam finite elements (FE). A discrete-to-continuum transformation is applied to the microscale unit cell and its strain energy density is expressed in terms of the macroscale 1-D beam kinematics. Then the constitutive equations for the micropolar web-core beam are derived assuming strain energy equivalence between the microscale unit cell and the macroscale beam. A micropolar beam FE model for static and dynamic problems is developed using a general solution of the beam equilibrium equations. A localization method for the calculation of periodic classical beam responses from micropolar results is given. The 1-D beam model is used in linear bending and vibration problems of 2-D web-core sandwich panels that have flexible joints. Localized 1-D results are shown to be in good agreement with experimental and 2-D FE beam frame results.Item Two-scale micropolar plate model for web-core sandwich panels(PERGAMON-ELSEVIER SCIENCE LTD, 2019-10-01) Karttunen, Anssi T.; Reddy, J. N.; Romanoff, Jani; Department of Mechanical Engineering; Marine Technology; Texas A&M UniversityA 2-D micropolar equivalent single-layer (ESL), first-order shear deformation (FSDT) plate model for 3-D web-core sandwich panels is developed. First, a 3-D web-core unit cell is modeled by classical shell finite elements. A discrete-to-continuum transformation is applied to the microscale unit cell and its strain and kinetic energy densities are expressed in terms of the macroscale 2-D plate kinematics. The hyperelastic constitutive relations and the equations of motion (via Hamilton’s principle) for the plate are derived by assuming energy equivalence between the 3-D unit cell and the 2-D plate. The Navier solution is developed for the 2-D micropolar ESL-FSDT plate model to study the bending, buckling, and free vibration of simply-supported web-core sandwich panels. In a line load bending problem, a 2-D classical ESL-FSDT plate model yields displacement errors of 34–175% for face sheet thicknesses of 2–10 mm compared to a 3-D FE solution, whereas the 2-D micropolar model gives only small errors of 2.7–3.4% as it can emulate the 3-D deformations better through non-classical antisymmetric shear behavior and local bending and twisting.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.