Optimization of elastic spring supports for cantilever beams

Aydın, Ersin; Dutkiewicz, Maciej; Öztürk, Baki; Sönmez, M. Kemal

doi:10.1007/s00158-019-02469-3

Cited by 31 publications

(13 citation statements)

References 41 publications

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“…By taking advantage of the theoretical formulation introduced by Belotti and Richiedei (2018), this paper proposes an integrated approach to EA for a cantilever beam controlled through a piezoelectric actuator and validates it experimentally. Beams are widely used as structural elements in many engineering problems, and the optimal design of these systems is still investigated in the very recent literature in the field of structural optimization, such as for example in Aydin et al (2020) or Hauser and Wang (2018). A different goal is investigated in this paper, and a new design method is proposed through a concurrent and multi-domain approach.…”

Section: Objectives and Contributions Of The Papermentioning

confidence: 99%

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Belotti

Richiedei

Trevisani

2020

Struct Multidisc Optim

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The paper proposes a multi-domain approach to the optimization of the dynamic response of an underactuated vibrating linear system through eigenstructure assignment, by exploiting the concurrent design of the mechanical properties, the regulator and state observers. The approach relies on handling simultaneously mechanical design and controller synthesis in order to enlarge the set of the achievable performances. The underlying novel idea is that structural properties of controlled mechanical systems should be designed considering the presence of the controller through a concurrent approach: this can considerably improve the optimization possibilities. The method is, first, developed theoretically. Starting from the definition of the set of feasible system responses, defined through the feasible mode shapes, an original formulation of the optimality criterion is proposed to properly shape the allowable subspace through the optimal modification of the design variables. A proper choice of the modifications of the elastic and inertial parameters, indeed, changes the space of the allowable eigenvectors that can be achieved through active control and allows obtaining the desired performances. The problem is then solved through a rank-minimization with constraints on the design variables: a convex optimization problem is formulated through the “semidefinite embedding lemma” and the “trace heuristics”. Finally, experimental validation is provided through the assignment of a mode shape and of the related eigenfrequency to a cantilever beam controlled by a piezoelectric actuator, in order to obtain a region of the beam with negligible oscillations and the other one with large oscillations. The results prove the effectiveness of the proposed approach that outperforms active control and mechanical design when used alone.

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Section: Objectives and Contributions Of The Papermentioning

confidence: 99%

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Belotti

Richiedei

Trevisani

2020

Struct Multidisc Optim

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“…Winkler’s hypothesis about the proportionality of stresses and discontinuities on the model interface [ 22 , 23 , 24 ] is very fruitful in problems considering the conjugation of continuums through a thin intermediate layer, and makes it possible to reduce the dimension of the problem. Examples of the successful application of this model are found in [ 44 , 45 , 46 , 47 ] for one-dimensional rod objects and [ 48 , 49 , 50 ] for two-dimensional structures. In particular, in dentistry, the Winkler layer can describe the behavior of periodontal tissues in the interaction of the dental root with the jaw [ 51 ].…”

Section: Introductionmentioning

confidence: 99%

Analytical Modeling of the Interaction of a Four Implant-Supported Overdenture with Bone Tissue

et al. 2022

Self Cite

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Today, an interdisciplinary approach to solving the problems of implantology is key to the effective use of intraosseous dental implantations. The functional properties of restoration structures for the dentition depend significantly on the mechanical stresses that occur in the structural elements and bone tissues in response to mastication loads. An orthopedic design with a bar fixation system connected to implants may be considered to restore an edentulous mandible using an overdenture. In this study, the problem of the mechanics of a complete overdenture based on a bar and four implants was formulated. A mathematical model of the interaction between the orthopedic structure and jawbone was developed, and a methodology was established for the analytical study of the stress state of the implants and adjacent bone tissue under the action of a chewing load. The novelty of the proposed model is that it operates with the minimum possible set of input data and provides adequate estimates of the most significant output parameters that are necessary for practical application. The obtained analytical results are illustrated by two examples of calculating the equivalent stresses in implants and the peri-implant tissue for real overdenture designs. To carry out the final assessment of the strength of the implants and bone, the prosthesis was loaded with mastication loads of different localization. In particular, the possibilities of loading the prosthesis in the area of the sixth and seventh teeth were investigated. Recommendations on the configuration of the distal cantilever of the overdenture and the acceptable level and distribution of the mastication load are presented. It was determined that, from a mechanical point of view, the considered orthopedic systems are capable of providing long-term success if they are used in accordance with established restrictions and recommendations.

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“…In [7,50], authors use a density approach, such as SIMP, to find the optimal supports configuration. Another example of supports modeled by elastic springs is investigated in [4]. The optimal locations and number of springs that support a vibrating cantilever beam are optimized to minimize the shear force applied to the beam.…”

Section: Introductionmentioning

confidence: 99%

Coupled topology optimization of structure and connections for bolted mechanical systems

Rakotondrainibe

Desai

Orval

et al. 2022

European Journal of Mechanics - A/Solids

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Optimization of elastic spring supports for cantilever beams

Cited by 31 publications

References 41 publications

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Analytical Modeling of the Interaction of a Four Implant-Supported Overdenture with Bone Tissue

Coupled topology optimization of structure and connections for bolted mechanical systems

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