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  • 51.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Finite element treatment of thermoelastic wear problems1998Inngår i: IUTAM Symposium on Unilateral Multibody Contacts: Proceedings of the IUTAM Symposium held in Munich, Germany, August 3-7, 1998 / [ed] G.M.L. Gladwell, F. Pfeiffer, Springer, 1998, s. 265-274Konferansepaper (Fagfellevurdert)
  • 52.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Finite element treatment of tribological problems2000Inngår i: Proceedings of the First International Symposium on Impact and Friction of Solids, Structures and Machines / [ed] Ardéshir Guran, Singapore: World Scientific, 2000, s. 277-280Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The present paper concerns the numerical treatment of contact, friction and wear between a thermoelastic body and a rigid foundation. The governing equations of thermoelasticity, Signorini contact, Coulomb friction and Archard wear are put together to a system of equations which is solved by using a Newton method.

  • 53.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Finite element treatment of two-dimensional thermoelastic wear problems1999Inngår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 177, nr 3-4, s. 441-455Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The present paper concerns the numerical treatment of thermoelastic wear problems. The governing equations of thermoelasticity coupled to Signorini contact, Coulomb's friction and Archard's wear are formulated as a system of discrete equations. This equation system is solved, using a Bouligand differentiable Newton method, for five problems of didactic nature.

  • 54.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Frictional Contact/Impact between a Hyperelastic Body and Moving Rigid Obstacles2006Inngår i: III European Conference on Computational Mechanics: Solids, Structures and Coupled Problems in Engineering: Book of Abstracts / [ed] C. A. Motasoares, J. A. C. Martins, H. C. Rodrigues, Jorge A. C. Ambrósio, C. A. B. Pin, Springer, 2006, s. 339-339Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper a method for frictional contact/impact between a hyperelastic body and moving rigid obstacles is suggested and investigated. The work is a further development of the suggested method in [1]. The motion of an obstacle is defined by a prescribed translation vector and a prescribed rotation matrix. The geometry of the obstacles are defined by smooth functions. Each function is formulated in a moving frame which is governed by the translation vector and the rotation matrix. These functions are then included in new formulations of Signorini’s conditions and Coulomb’s law of friction. Instead of using contact forces, the mean value impulses are utilized in these formulations, which also are adopted in the law of motion which is given on velocity form. By following this approach, no search algorithm is needed, the normal and tangential directions are well defined and the treatment of non-constant transformation matrices in the law of motion is straight-forward. A total Lagrangian formulation of the system is given. The elastic properties of the body are defined by coupling the second Piola-Kirchhoff stress to the Green-Lagrange strain via the Kirchhoff-St.Venant law. The governing equations are solved by a nonsmooth Newton method. This is performed by following the augmented Lagrangian approach and deriving the consistent stiffness matrix as well as the contact stiffness matrices. The method is implemented in TriLab. TriLab is a user-friendly finite element toolbox for simulating contact and impact problems. TriLab is developed using Matlab and Visual Fortran. The Fortran code is linked to Matlab as mex-files. The code is vectorized and the sparsity is utilized. By using Trilab, the presented method will be demonstrated by solving two-dimensional problems.

  • 55.
    Strömberg, Niclas
    School of Engineering, Jönköping University, Jönköping, Sweden.
    RBDO with Non-Gaussian Variables by using a LHS- and SORM-based SLP approach and Optimal Regression Models2012Inngår i: 3rd International Conference on Engineering Optimization, 2012Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    A general sequential linear programming (SLP) approach for reliability based design optimization (RBDO) with non-Gaussian random variables is presented. The RBDO problems are formulated by using optimal regression models (ORM) as surrogate models and S-optimal design of experiments (DoE). The S-optimal DoE is obtained by maximizing the average mean of the distances between the nearest neighbors. Finite element simulations are performed for the S-optimal DoE and corresponding ORM are obtained by a genetic algorithm. In such manner not only optimal regression coefficients are generated but also optimal rational base functions. The RBDO problems are solved by introducing intermediate variables defined by the iso-probabilistic transformation at the most probable point. By using these variables in the Taylor expansions, a corresponding deterministic linear programming problem is derived, which is corrected by applying second order reliability methods (SORM) as well as Monte Carlo simulations. For low target values on the reliability crude Monte Carlo simulations are used, but for high targets a Latin hypercube sampling (LHS) approach is utilized. The implementation of the suggested sampling- and SORM-based SLP approach is efficient and robust. This is demonstrated by presenting trade-off curves between the objective function, constraints, variables and the target of reliability.

  • 56.
    Strömberg, Niclas
    Örebro universitet, Institutionen för naturvetenskap och teknik. Örebro University.
    Reliability-based Design Optimization by using Ensemble of Metamodels2019Konferansepaper (Fagfellevurdert)
  • 57.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Simulation of Rotary Draw Bending using Abaqus and a Neural Network2005Inngår i: Proceedings of Nafems Nordic Conference on Component and System Analysis using Numerical Simulation Techniques - FEA, CFD, MBS, 2005Konferansepaper (Fagfellevurdert)
  • 58.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    The Influence of Sliding Friction on Optimal Topologies2013Inngår i: Recent Advances in Contact Mechanics: Papers Collected at the 5th Contact Mechanics International Symposium (CMIS2009), Springer Berlin/Heidelberg, 2013, Vol. 56, s. 327-336Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper the influence of sliding friction on optimal topologies is investigated and some preliminary results are presented. A design domain unilaterally constrained by a spinning support is considered. Most recently, Stromberg and Klarbring have developed methods for performing topology optimization of linear elastic structures with unilateral contact conditions. In this works sliding friction is also included in the contact model. In such manner it is possible to study how the spinning of the support will influence the optimal design. This was not possible before. The support is modeled by Signorini's contact conditions and Coulomb's law of friction. Signorini's contact conditions are regularized by a smooth approximation, which must not be confused with the well-known penalty approach. The state of the system, which is defined by the equilibrium equations and the smooth approximation, is solved by a Newton method. The design parametrization is obtained by using the SIMP-model. The minimization of compliance for a limited value of volume is considered. The optimization problem is solved by a nested approach where the equilibrium equations are linearized and sensitivities are calculated by the adjoint method. The problem is then solved by SLP, where the LP-problem is solved by an interior point method that is available in the package of Mat lab. In order to avoid mesh-dependency and patterns of checker-boards the sensitivities are filtered by Sigmund's filter. The method is implemented by using Mat lab and Visual Fortran, where the Fortran code is linked to Mat lab as mex-files. The implementation is done for a general design domain in 2D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.

  • 59.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Topology Optimization of Bodies in Unilateral Contact by Maximizing the Potential Energy2012Inngår i: Proceedings the Eleventh International Conferenceon Computational Structures Technology / [ed] B.H.V. Topping, Kippen, Stirlingshire: Civil-Comp Proceedings , 2012, s. Paper 237-Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The modelling of the boundary conditions is crucial in topology optimisation. Small changes in these conditions will typically imply new optimal layouts of material. In many situations the design domain is connected to an assembly of components using contact interfaces. In order to generate proper layouts for this type of design domain one must treat these contact interfaces accurately in the topology optimisation procedure.

    The bottle-neck in topology optimisation of non-linear structural problems, such as contact problems, is to solve the state equations and the adjoint equations. By choosing the potential energy as the objective the latter equations are not needed in the sensitivity analysis. In this paper topology optimization of contact problems including non-zero prescribed displacements by maximizing the potential energy is performed. For contact problems with zero initial contact gaps and zero prescribed displacements this is equivalent to minimising the compliance, which is the standard approach in topology optimisation. However, when the compliance is used as objective in topology optimisation of contact problems an extra adjoint equation must be solved. This is not needed in the formulation presented in this paper.

    The efficiency of the approach is demonstrated by studying three different problems, two problems in two-dimensions and one in a three-dimensional setting. The method is implemented by using Matlab and Intel Fortran, where the Fortran code is linked to Matlab as mex-files. The implementation can be downloaded as a toolbox (Topo4abq). The three problems have beensolved using this toolbox on a laptop with an Intel Core i7 2.67 GHz processor and a 64 bit version of Windows. It is shown that the CPU-time is reduced as much as 25% compared to an adjoint approach developed in previous works.

  • 60.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Topology Optimization of Non-linear Elastic Structures by using SLP2010Inngår i: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009: Volume 5: 35th Design Automation Conference, Parts A and B, ASME Press, 2010, s. 1261-1265Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper a method for topology optimization of nonlinear elastic structures is suggested. The method is developed by starting from a total Lagrangian formulation of the system. The internal force is defined by coupling the second Piola-Kirchhoff stress to the Green-Lagrange strain via the Kirchhoff-St. Venant law. The state of equilibrium is obtained by first deriving the consistency stiffness matrix and then using Newton's method to solve the non-linear equations. The design parametrization of the internal force is obtained by adopting the SIMP approach. The minimization of compliance for a limited value of volume is considered. The optimization problem is solved by SLP. This is done by using a nested approach where the equilibrium equation is linearized and the sensitivity of the cost Junction is calculated by the adjoint method. In order to avoid mesh-dependency the sensitivities are filtered by Sigmund'sfilter. The final LP-problem is solved by an interior point method that is available in Matlab. The implementation is done for a general design domain in 2D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.

  • 61.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Topology optimization of structures with manufacturing and unilateral contact constraints by minimizing an adjustable compliance–volume product2010Inngår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 42, nr 3, s. 341-350Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper the concept of extended optimality, or hyperoptimality, is adopted. By following this idea, a new compliance-volume product is suggested as objective. The volume appearing in the product is also raised to the power of a new design parameter which can be set to different values. In such manner design concepts with different volume fractions can be generated by using the approach of extended optimality. Both manufacturing constraints and unilateral contact constraints are included in the proposed method. The manufacturing constraints are implemented by adjusting the move limits such that the draw directions are satisfied. Both one draw direction as well as split draw constraints are considered. The contact conditions are modeled by the augmented Lagrangian approach such that the Jacobian in the Newton algorithm as well as in the adjoint equation becomes symmetric. The design parametrization is done by the SIMP model and Sigmund's filter is utilized when the sensitivities are calculated. The proposed method is very robust and efficient. This is demonstrated by solving problems in both 2D and 3D. The numerical results are also compared to solutions obtained by performing compliance optimization with a constraint on the volume fraction.

  • 62.
    Strömberg, Niclas
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Topology Optimization of Two Linear Elastic Bodies in Unilateral Contact2010Inngår i: Proceedings of the 2nd International Conference on Engineering Optimization, 2010Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The optimal solutions are most sensitive to the boundary conditions when performing topology optimization of components. In many applications the design domain of the components are subjected to unilateral contact conditions. In order to obtain relevant conceptual designs by topology optimization of such systems, the contact conditions should be included explicitly in the optimization. Recently, in a number of works by Strömberg and Klarbring, such a method has been developed for one elastic body unilateral constrained to rigid supports. Here, this approach is extended such that a system of two elastic bodies in unilateral contact is considered. For this systems the compliance is minimized by adopting the SIMP-model. A nested formulation of the problem is solved by SLP, where the sensitivities are obtained by solving an adjoint equation. In this latter equation, the Jacobian from the Newton method used to solve the state problem appears. The state problem is treated by an augmented Lagrangian formulation of the bodies in contact. Thus, the Jacobian is simply the gradient of the corresponding system of equations to this formulation. The method is implemented in the toolbox Topo4abq by using Matlab and Intel Fortran. The method is both efficient and robust. This is demonstrated by solving several 2D-problems. The results are also compared to the solutions obtained when the contact conditions are treated by joining the two bodies to one body. In a near future3D-problems will also be solved by using the presented approach.

  • 63.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    TriLab: a tool for simulating tribological systems2003Inngår i: Proceedings of the 9th International Power Transmission and Gearing Conference, New York: American Society of Mechanical Engineers , 2003, s. 1051-1056Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper TriLab is presented. TriLab is a user-friendly finite element tool for simulating tribological systems. TriLab is based on a method for structural dynamic contact problems with friction and wear. The method is reviewed in the paper as well as the quasi-static formulation of frictional contact, the energy-momentum conserving approach of Simo and Tarnow, and Moreau's nonsmooth contact dynamics formulation. TriLab is easy to use and can be utilized for solving both small displacement contact, rolling contact as well as impact problems. This is demonstrated by solving a number of examples.

  • 64.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    TriLab: a toolbox for tribological systems2003Inngår i: Proceedings from the Nordic MATLAB Conference 2003, Copenhagen, Denmark, 2003Konferansepaper (Fagfellevurdert)
  • 65.
    Strömberg, Niclas
    Jönköping University, Jönköping, Sweden.
    What is the optimal shape of a snap ring?2008Inngår i: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (DETC2007): Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Part A, New York: American Society of Mechanical Engineers , 2008, s. 407-412Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper a non-linear elastic ring is studied by using a method for contact/impact problems. The method is developed for frictional contact, impact and rolling between a two-dimensional hyperelastic body and rigid foundations. The elastic properties of the body are defined by coupling the second Piola-Kirchhoff stress to the Green-Lagrange strain via the Kirchhoff-St. Venant law. The rigid supports are described by smooth functions. By introducing the mean value impulses, these functions are utilized to formulate new contact/impact laws. The support functions appear explicitly in the variational formulation of Signorini, and implicitly in the maximal dissipation principle of Coulomb. A feature of this approach is that no search algorithm is needed. Another feature is that the normal and tangential directions of the supports are well defined The above constitutive assumptions together with the law of motion, which is written on velocity form, define the governing equations of the system. These are solved by a nonsmooth Newton method. The method is utilized to study the contact pressure between a snap ring and a rigid groove which has the shape of a perfect circle. It is obvious that if the snap ring also has the shape of a perfect circle, then the distribution of the contact pressure will be uneven. An even distribution of the contact pressure is preferable in order to improve function and increase lifetime. The question that is considered in this paper is how the shape of the ring should be designed in order to produce this type of contact pressure.

  • 66.
    Strömberg, Niclas
    et al.
    Linköping university, Linköping, Sweden.
    Johansson, Lars
    Klarbring, Anders
    A generalized standard model for contact, friction and wear1995Inngår i: Contact Mechanics: Proceedings of the 2nd Contact Mechanics International Symposium, New York: Plenum Press , 1995, s. 327-334Konferansepaper (Fagfellevurdert)
  • 67.
    Strömberg, Niclas
    et al.
    Department of Mechanical Engineering, Division of Mechanics, Linköping Inst. of Technology, Linköping, Sweden.
    Johansson, Lars
    Department of Mechanical Engineering, Division of Mechanics, Linköping Inst. of Technology, Linköping, Sweden.
    Klarbring, Anders
    Department of Mechanical Engineering, Division of Mechanics, Linköping Inst. of Technology, Linköping, Sweden.
    Derivation and analysis of a generalized standard model for contact, friction and wear1996Inngår i: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 33, nr 13, s. 1817-1836Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A model for mechanical contact including friction, wear and heat generation is proposed. By defining an internal state variable for the wear process, a generalized standard model for contact, friction and wear is derived from the principle of virtual power and the fundamental laws of thermodynamics. Within the frame of the generalized standard model some specific constitutive models are presented. For instance, a free energy corresponding to an extension of Signorini's unilateral contact conditions to include the wear process at the interface and having a linear tangential compliance between the relative tangential displacement and the tangential contact traction is suggested. Furthermore, a dual pseudo-potential with a friction and wear limit criterion in agreement with Coulomb's law of friction Archard's law of wear is given. In order to study existence and uniqueness questions, this pair of free energy and dual pseudo-potential is analysed in a one point elastic quasi-static contact problem with two degrees of freedom and thermal effects neglected. The so-called rate problem is solved.

  • 68.
    Strömberg, Niclas
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Klarbring, Anders
    Division of Mechanics, Linköping University, Linköping, Sweden.
    Minimization of Compliance of a Linear Elastic Structure with Contact Constraints by using Sequential Linear Programming and Newton's method2008Inngår i: Proceedings of the 7th International ASMO-UK/ISSMO International Conference on Engineering Design Optimization, 2008, s. 379-386Konferansepaper (Fagfellevurdert)
  • 69.
    Strömberg, Niclas
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Klarbring, Anders
    Division of Mechanics, Linköping University, Linköping, Sweden.
    Topology optimization of structures in unilateral contact2010Inngår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 41, nr 1, s. 57-64Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper a general framework for topology optimization of structures in unilateral contact is developed. A linear elastic structure that is unilaterally constrained by rigid supports is considered. The supports are modeled by Signorini's contact conditions which in turn are treated by the augmented Lagrangian approach as well as by a smooth approximation. The latter approximation must not be confused with the well-known penalty approach. The state of the system, which is defined by the equilibrium equation and the two different contact formulations, is solved by a Newton method. The design parametrization is obtained by using the SIMP-model. The minimization of compliance for a limited value of volume is considered. The optimization problems are solved by SLP. This is done by using a nested approach where the state equations are linearized and sensitivities are calculated by the adjoint method. In order to avoid mesh-dependency the sensitivities are filtered by Sigmund's filter. The final LP-problem is solved by an interior point method that is available in Matlab. The implementation is done for a general design domain in 2D as well as in 3D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.

  • 70.
    Strömberg, Niclas
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Klarbring, Anders
    Division of Mechanics, Linköping University, Linköping, Sweden.
    Topology optimization of Structures with Contact Constraints by using a Smooth Formulation and a Neested Approach2009Inngår i: Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization, International Society for Structural and Multidisciplinary Optimization , 2009Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper a method for topology optimization of structures in unilateral contact is developed. A linear elastic structure that is unilateral constrained by rigid supports is considered. The supports are modeled by Signorini’s contact conditions which in turn are treated by a smooth approximation. This approximation must not be confused with the well-known penalty approach. The state of the system, which is defined by the equilibrium equations and the smooth approximation, is solved by a Newton method. The design parametrization is obtained by using the SIMP-model. The minimization of compliance for a limited value of volume is considered. The optimization problem is solved by a nested approach where the equilibrium equations are linearized and sensitivities are calculated by the adjoint method. The problem is then solved by SLP. The LP-problem is in turn solved by an interior point method that is available in Matlab. In order to avoid mesh-dependency the sensitivities are filtered by Sigmund’s filter. The method is implemented by using Matlab and Visual Fortran, where the Fortran code is linked to Matlab as mex-files. The implementation is done for a general design domain in 2D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.

  • 71.
    Strömberg, Niclas
    et al.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    Massana, J. F.
    Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden.
    A soft contact formulation for modelling thin coatings2005Inngår i: Computer methods and experimental measurements for surface effects and contact mechanics VII / [ed] J.T.M. De Hosson, C.A. Brebbia, S.-I. Nishida, Southampton: WIT Press, 2005, s. 211-218Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Today, high-performance machine components are often improved by coatings. For instance, thin layers can increase the life-time by reducing friction and wear. An example of this is the spline joint in the suspension system of a truck. This joint, which is placed at the output of the gearbox, allows relative translation in the axial direction. In order to improve performance, this spline can be coated with a thin layer of polyamide. In such a manner, the life-time of the joint is increased by decreasing friction and wear. This type of coatings may be optimized by performing finite element contact analysis. However, when performing such an analysis, it can be difficult to obtain a good mesh due to the very thin layer. An approach to avoid this difficulty is to instead include the elastic properties of the coating in the contact formulation. Such a soft contact formulation is suggested and solved in this paper. The formulation is obtained by adding an elastic part to the free energy corresponding to Signorini’s contact conditions. In such a manner a new soft contact law is derived by taking the subdifferential of the free energy. In this law two new constitutive parameters appear. The first parameter describes the elastic response of the thin layer and the second one is taken to be equal to the thickness of the layer. In the event, when the layer is completely penetrated, hard contact is developed following a classical Lagrange formulation of Signorini.A numerical method for solving the new contact formulation is also developed. The method is obtained by following the augmented Lagrangian approach. In such a way an equivalent setting of equations is derived which in turn is solved by using a non-smooth Newton method. The method is implemented in a Matlab toolbox. The method is robust and produces accurate results. This is shown by comparing numerical results with solutions obtained by using a penalty formulation in Abaqus.

  • 72.
    Tapankov, Martin
    et al.
    School of Engineering, JTH. Research area Product Development - Simulation and Optimization, Jönköping University, Jönköping, Sweden.
    Strömberg, Niclas
    School of Engineering, JTH. Research area Product Development - Simulation and Optimization, Jönköping University, Jönköping, Sweden.
    Sampling- and SORM-based RBDO of a Knuckle Component by using Optimal Regression Models2012Inngår i: Proceedings of the 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, American Institute of Aeronautics and Astronautics, 2012Konferansepaper (Fagfellevurdert)
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