Flexure joints are rapidly gaining ground in precision engineering because of their predictable behavior. However the range of motion of flexure joints is limited due to loss of support stiffness in deformed configurations. Most of the common flexure joints consist of prismatic leaf springs. This paper presents a simple non-prismatic beam formulation that can be used for the efficient modelling of non-prismatic leaf springs. The resulting stiffness and stress computed by the non-prismatic beam element are compared to the results of a finite element analysis. The paper shows that the support stiffness of two typical flexure joints can be increased up to a factor of 1.9 by using non-prismatic instead of prismatic leaf springs.
{"title":"A Non-Prismatic Beam Element for the Optimization of Flexure Mechanisms","authors":"K. Dwarshuis, R. Aarts, M. Ellenbroek, D. Brouwer","doi":"10.1115/detc2020-22242","DOIUrl":"https://doi.org/10.1115/detc2020-22242","url":null,"abstract":"\u0000 Flexure joints are rapidly gaining ground in precision engineering because of their predictable behavior. However the range of motion of flexure joints is limited due to loss of support stiffness in deformed configurations. Most of the common flexure joints consist of prismatic leaf springs. This paper presents a simple non-prismatic beam formulation that can be used for the efficient modelling of non-prismatic leaf springs. The resulting stiffness and stress computed by the non-prismatic beam element are compared to the results of a finite element analysis. The paper shows that the support stiffness of two typical flexure joints can be increased up to a factor of 1.9 by using non-prismatic instead of prismatic leaf springs.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115290091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Flexure based compliant mechanisms suited for a large range of motion can be designed by handling the challenges arising from combining low compliance in the desired directions, high support stiffness, low stresses and high unwanted natural frequencies. Current topology optimization tools typically can’t model large deflections of flexures, are too conceptual or are case specific. In this research, a new spatial topological synthesis algorithm based on building blocks is proposed to optimize the performance of an initial design. The algorithm consists of successive shape optimizations and layout syntheses. In each shape optimization the dimensions for some layout are optimized. The layout synthesis strategically replaces the most “critical” building block with a better option. To maximize the first unwanted natural frequency the replacement strategy depends the strain energy distribution of the accompanying mode shape. The algorithm is tested for the design of a 1-DOF flexure hinge. The obtained final layout agrees with results known from literature.
{"title":"Building Block Based Topology Synthesis Algorithm to Optimize the Natural Frequency in Large Stroke Flexure Mechanisms","authors":"Mathijs E. Fix, D. Brouwer, R. Aarts","doi":"10.1115/detc2020-22393","DOIUrl":"https://doi.org/10.1115/detc2020-22393","url":null,"abstract":"\u0000 Flexure based compliant mechanisms suited for a large range of motion can be designed by handling the challenges arising from combining low compliance in the desired directions, high support stiffness, low stresses and high unwanted natural frequencies. Current topology optimization tools typically can’t model large deflections of flexures, are too conceptual or are case specific. In this research, a new spatial topological synthesis algorithm based on building blocks is proposed to optimize the performance of an initial design. The algorithm consists of successive shape optimizations and layout syntheses. In each shape optimization the dimensions for some layout are optimized. The layout synthesis strategically replaces the most “critical” building block with a better option. To maximize the first unwanted natural frequency the replacement strategy depends the strain energy distribution of the accompanying mode shape. The algorithm is tested for the design of a 1-DOF flexure hinge. The obtained final layout agrees with results known from literature.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130440502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dynamics of axially moving continua, such as beams, cables and strings, can be modeled by use of an Arbitrary La-grangian Eulerian (ALE) approach. Within a Finite Element framework, an ALE element is indeed a non-material system, i.e. a mass flow occurs at its boundaries. This article presents the dynamic description of such systems and highlights the peculiarities that arise when applying standard mechanical principles to non-material systems. Starting from D’Alembert’s principle, Hamilton’s principle and Lagrange’s equations for a non-material system are derived and the significance of the additional transport terms discussed. Subsequently, the numerical example of a length-changing beam is illustrated. Energetic considerations show the complex dynamic behavior non-material systems might exhibit.
{"title":"Variational Principles for Non-Material Systems Within an Arbitrary Lagrangian Eulerian Description of Motion","authors":"G. Pennisi, O. Bauchau","doi":"10.1115/detc2020-22494","DOIUrl":"https://doi.org/10.1115/detc2020-22494","url":null,"abstract":"\u0000 Dynamics of axially moving continua, such as beams, cables and strings, can be modeled by use of an Arbitrary La-grangian Eulerian (ALE) approach. Within a Finite Element framework, an ALE element is indeed a non-material system, i.e. a mass flow occurs at its boundaries. This article presents the dynamic description of such systems and highlights the peculiarities that arise when applying standard mechanical principles to non-material systems. Starting from D’Alembert’s principle, Hamilton’s principle and Lagrange’s equations for a non-material system are derived and the significance of the additional transport terms discussed. Subsequently, the numerical example of a length-changing beam is illustrated. Energetic considerations show the complex dynamic behavior non-material systems might exhibit.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133474860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guanchu Chen, Hiroki Yamashita, Y. Ruan, P. Jayakumar, H. Sugiyama
Scalable parallel computing schemes play an important role in physics-based off-road mobility simulations due to complexities in modeling soil behavior for vehicle-terrain interaction. With the hierarchical multiscale off-road mobility simulation capability, limitations of existing computational deformable terrain models can be eliminated, including the use of phenomenological constitutive assumptions in finite element (FE) approaches as well as high computational intensity of discrete element (DE) models. However, parallel computing algorithms for multiscale simulations need to be carefully developed due to possible unbalanced computational loads occurring in lower-scale RVE simulations, which prevents desirable computational speedup. Therefore, this study aims to develop a scalable hybrid MPI-OpenMP parallel computing framework for hierarchical FE-DE multiscale off-road mobility simulations with a special focus on computational load balancing for the lower-scale DE models.
{"title":"Multiscale Off-Road Mobility Simulation With Computational Load Balancing for Lower-Scale Discrete-Element Models","authors":"Guanchu Chen, Hiroki Yamashita, Y. Ruan, P. Jayakumar, H. Sugiyama","doi":"10.1115/detc2020-22195","DOIUrl":"https://doi.org/10.1115/detc2020-22195","url":null,"abstract":"\u0000 Scalable parallel computing schemes play an important role in physics-based off-road mobility simulations due to complexities in modeling soil behavior for vehicle-terrain interaction. With the hierarchical multiscale off-road mobility simulation capability, limitations of existing computational deformable terrain models can be eliminated, including the use of phenomenological constitutive assumptions in finite element (FE) approaches as well as high computational intensity of discrete element (DE) models. However, parallel computing algorithms for multiscale simulations need to be carefully developed due to possible unbalanced computational loads occurring in lower-scale RVE simulations, which prevents desirable computational speedup. Therefore, this study aims to develop a scalable hybrid MPI-OpenMP parallel computing framework for hierarchical FE-DE multiscale off-road mobility simulations with a special focus on computational load balancing for the lower-scale DE models.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133905757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rotorcraft-Pilot-Coupling (RPC) is a dynamic phenomenon in which the rotorcraft vibrations are transmitted through the cockpit, the seat and the control inceptors to the helicopter pilot and to the passengers. Handling qualities are affected by the proneness of the of rotorcraft to give rise to adverse interactions, an unwanted quality that can be captured by the so called biodynamic feedthrough. In this work, a multibody model of the whole upper body, developed by the authors, is used in order of evaluate the effects of several parameters influencing cockpit layout design: namely, the pilot seat backrest angle, compliance, and connection to the cockpit floor. As a representative parameter of the flight controls design, the effects related to the characteristics of the trim spring is also investigated. Simulations encompass subjects of different anthropometric data, in order to represent possible intra-subject variations. Biomechanical feedthroughs at the collective and cyclic commands, in response to vertical acceleration inputs, are discussed, along with single-harmonic, high magnitude input responses that highlight the presence and importance of nonlinear effects.
{"title":"Effects of Flight Controls and Cockpit Layout Design in Rotorcraft-Pilot Couplings: A Computational Approach","authors":"A. Cocco, A. Zanoni, V. Muscarello, P. Masarati","doi":"10.1115/detc2020-22304","DOIUrl":"https://doi.org/10.1115/detc2020-22304","url":null,"abstract":"\u0000 Rotorcraft-Pilot-Coupling (RPC) is a dynamic phenomenon in which the rotorcraft vibrations are transmitted through the cockpit, the seat and the control inceptors to the helicopter pilot and to the passengers. Handling qualities are affected by the proneness of the of rotorcraft to give rise to adverse interactions, an unwanted quality that can be captured by the so called biodynamic feedthrough. In this work, a multibody model of the whole upper body, developed by the authors, is used in order of evaluate the effects of several parameters influencing cockpit layout design: namely, the pilot seat backrest angle, compliance, and connection to the cockpit floor. As a representative parameter of the flight controls design, the effects related to the characteristics of the trim spring is also investigated. Simulations encompass subjects of different anthropometric data, in order to represent possible intra-subject variations. Biomechanical feedthroughs at the collective and cyclic commands, in response to vertical acceleration inputs, are discussed, along with single-harmonic, high magnitude input responses that highlight the presence and importance of nonlinear effects.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133544037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rigid bodies are an essential part of multibody systems. As there are six degrees of freedom in rigid bodies, it is natural but also precarious to use three parameters for the displacement and three parameters for the rotation parameters — since there is no singularity-free description of spatial rotations based on three rotation parameters. Standard formulations based on three rotation parameters avoid singularities, e.g. by applying reparameterization strategies during the time integration of the rotational kinematic equations. Alternatively, Euler parameters are commonly used to avoid singularities. State of the art approaches use Lie group methods, specifically integrators, to model rigid body motion without the need for the above mentioned solutions. However, the methods so far have been based on additional information, e.g., the rotation matrix, which has to been computed in each step. The latter procedure is thus difficult to be implemented in existing codes that are based on three rotation parameters. In this paper, we use the rotation vector to model large rotations. Whereby Lie group integration methods are used to compute consistent updates for the rotation vector in every time step. The resulting rotation vector update is finite, while the derivative of the rotation vector in the singularity becomes unbounded. The advantages of this method are shown in an example of a gyro. Additionally, the method is applied to a multibody system and the effects of crossing singularities are presented.
{"title":"Explicit Time Integration of Multibody Systems Modelled With Three Rotation Parameters","authors":"S. Holzinger, J. Gerstmayr","doi":"10.1115/detc2020-22261","DOIUrl":"https://doi.org/10.1115/detc2020-22261","url":null,"abstract":"\u0000 Rigid bodies are an essential part of multibody systems. As there are six degrees of freedom in rigid bodies, it is natural but also precarious to use three parameters for the displacement and three parameters for the rotation parameters — since there is no singularity-free description of spatial rotations based on three rotation parameters. Standard formulations based on three rotation parameters avoid singularities, e.g. by applying reparameterization strategies during the time integration of the rotational kinematic equations. Alternatively, Euler parameters are commonly used to avoid singularities. State of the art approaches use Lie group methods, specifically integrators, to model rigid body motion without the need for the above mentioned solutions. However, the methods so far have been based on additional information, e.g., the rotation matrix, which has to been computed in each step. The latter procedure is thus difficult to be implemented in existing codes that are based on three rotation parameters. In this paper, we use the rotation vector to model large rotations. Whereby Lie group integration methods are used to compute consistent updates for the rotation vector in every time step. The resulting rotation vector update is finite, while the derivative of the rotation vector in the singularity becomes unbounded. The advantages of this method are shown in an example of a gyro. Additionally, the method is applied to a multibody system and the effects of crossing singularities are presented.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132654404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Huimin Zhang, Runsen Zhang, A. Zanoni, P. Masarati
A novel single-step time integration method is proposed for general dynamic problems. From linear spectral analysis, the new method with optimal parameters has second-order accuracy, unconditional stability, controllable algorithmic dissipation and zero-order overshoot in displacement and velocity. Comparison of the proposed method with several representative implicit methods shows that the new method has higher accuracy than the single-step generalized-α method, and also than the composite P∞-Bathe method when mild algorithmic dissipation is used. Besides, this method is spectrally identical to the linear two-step method, although being easier to use since it does not need additional start-up procedures. Its numerical properties are assessed through numerical examples, and the new method shows competitive performance for both linear and nonlinear problems.
{"title":"A Novel Single-Step Unconditionally Stable Numerical Integration Scheme With Tunable Algorithmic Dissipation","authors":"Huimin Zhang, Runsen Zhang, A. Zanoni, P. Masarati","doi":"10.1115/detc2020-22189","DOIUrl":"https://doi.org/10.1115/detc2020-22189","url":null,"abstract":"\u0000 A novel single-step time integration method is proposed for general dynamic problems. From linear spectral analysis, the new method with optimal parameters has second-order accuracy, unconditional stability, controllable algorithmic dissipation and zero-order overshoot in displacement and velocity. Comparison of the proposed method with several representative implicit methods shows that the new method has higher accuracy than the single-step generalized-α method, and also than the composite P∞-Bathe method when mild algorithmic dissipation is used. Besides, this method is spectrally identical to the linear two-step method, although being easier to use since it does not need additional start-up procedures. Its numerical properties are assessed through numerical examples, and the new method shows competitive performance for both linear and nonlinear problems.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121424127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Runsen Zhang, Huimin Zhang, A. Zanoni, A. Tasora, P. Masarati
To tackle coupled problems between smooth multibody systems and particle dampers, co-simulation between two general-purpose multibody codes is carried out, where the coupled system is decomposed by the force/displacement technique, and integrated by a loose coupling scheme or a tight one with iterative process. The stability properties of the coupling schemes are discussed using a two-mass oscillator, and it follows that the tight coupling scheme is more stable than the loose one, as expected. Besides, results also denote that the stability is influenced by the parameters of the integrator in each solver. Finally, the co-simulation schemes are applied to a simple system coupled with a particle damper, and the comparison among results obtained by co-simulation, monolithic simulation and experiments verifies the effectiveness of the proposed co-simulation scheme.
{"title":"Smooth/Non-Smooth Multibody Co-Simulation of a Particle Damper","authors":"Runsen Zhang, Huimin Zhang, A. Zanoni, A. Tasora, P. Masarati","doi":"10.1115/detc2020-22258","DOIUrl":"https://doi.org/10.1115/detc2020-22258","url":null,"abstract":"\u0000 To tackle coupled problems between smooth multibody systems and particle dampers, co-simulation between two general-purpose multibody codes is carried out, where the coupled system is decomposed by the force/displacement technique, and integrated by a loose coupling scheme or a tight one with iterative process. The stability properties of the coupling schemes are discussed using a two-mass oscillator, and it follows that the tight coupling scheme is more stable than the loose one, as expected. Besides, results also denote that the stability is influenced by the parameters of the integrator in each solver. Finally, the co-simulation schemes are applied to a simple system coupled with a particle damper, and the comparison among results obtained by co-simulation, monolithic simulation and experiments verifies the effectiveness of the proposed co-simulation scheme.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"285 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122974566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The application of the finite element method to the modeling of Cosserat solids is investigated in detail. In two- and three-dimensional elasticity problems, the nodal unknowns are the components of the displacement vector, which form a linear field. In contrast, when dealing with Cosserat solids, the nodal unknowns form the special Euclidean group SE(3), a nonlinear manifold. This observation has numerous implications on the implementation of the finite element method and raises numerous questions: (1) What is the most suitable representation of this nonlinear manifold? (2) How is it interpolated over one element? (3) How is the associated strain field interpolated? (4) What is the most efficient way to obtain the discrete equations of motion? All these questions are, of course intertwined. This paper shows that reliable schemes are available for the interpolation of the motion and curvature fields. The interpolated fields depend on relative nodal motions only, and hence, are both objective and tensorial. Because these schemes depend on relative nodal motions only, only local parameterization is required, thereby avoiding the occurrence of singularities. For Cosserat solids, it is preferable to perform the discretization operation first, followed by the variation operation. This approach leads to considerable computation efficiency and simplicity.
{"title":"Finite Element Models for Flexible Cosserat Solids","authors":"O. Bauchau, M. Shan","doi":"10.1115/detc2020-22134","DOIUrl":"https://doi.org/10.1115/detc2020-22134","url":null,"abstract":"\u0000 The application of the finite element method to the modeling of Cosserat solids is investigated in detail. In two- and three-dimensional elasticity problems, the nodal unknowns are the components of the displacement vector, which form a linear field. In contrast, when dealing with Cosserat solids, the nodal unknowns form the special Euclidean group SE(3), a nonlinear manifold. This observation has numerous implications on the implementation of the finite element method and raises numerous questions: (1) What is the most suitable representation of this nonlinear manifold? (2) How is it interpolated over one element? (3) How is the associated strain field interpolated? (4) What is the most efficient way to obtain the discrete equations of motion? All these questions are, of course intertwined. This paper shows that reliable schemes are available for the interpolation of the motion and curvature fields. The interpolated fields depend on relative nodal motions only, and hence, are both objective and tensorial. Because these schemes depend on relative nodal motions only, only local parameterization is required, thereby avoiding the occurrence of singularities. For Cosserat solids, it is preferable to perform the discretization operation first, followed by the variation operation. This approach leads to considerable computation efficiency and simplicity.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121628001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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