Shape optimization with the biological growth method: a parameter study

Tekkaya, A. Erman; Güneri, Alper

doi:10.1108/02644409610152989

Cited by 14 publications

(6 citation statements)

References 7 publications

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“…As expected, the ratio of the major to minor axes of the resulting ellipse is 1.976, which is extremely close to the analytical solution for infinite plate with an ellipse with the aspect ratio of 2:1. For the present case, the minimum possible uniform stress level along the boundary of an elliptical hole in an infinite plat is 67.5MPa [11]. For present results, the Von Mises stress along the design boundary is an essentially constant level with a range 68.78-69.96MPa, which is a little larger than the result in the infinite plate.…”

Section: Numerical Examplesmentioning

confidence: 43%

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A Relative-Stress Based Method for Structural Shape Optimization

2013

AMM

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A gradientless method for two-dimensional shape optimization is developed based on the magnitude of local relative-stress difference along the design boundary. The design boundary is modeled by using cubic splines, which are determined by a number of control points. The optimal shape of a design boundary with constant stress is achieved iteratively by moving control points consecutively (correspondingly, changing the shape of the design boundary) by an amount depending on the relative-stress difference between two neighboring boundary points. The key feature of the optimization method is that no arbitrary threshold stress is required. The result quality in terms of accuracy and efficiency are tested and discussed with several finite element analysis examples.

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Section: Numerical Examplesmentioning

confidence: 43%

“…A common strategy for gradientless based approaches to achieve a constant stressed boundary is to add material where stresses are high and remove it where stresses are low [5][6][7][8][9][10][11][12]. After that, a criterion to determine "high stress" and "low stress" should be specified clearly while using above assumptions.…”

Section: Introductionmentioning

confidence: 99%

A Relative-Stress Based Method for Structural Shape Optimization

2013

AMM

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“…16,17,48,49 In many structural shape optimization procedures, the parameters relate to specific design criteria 47,50 or are selected to control numerical stability. 51 However, these experimentally based or problem-specific means of defining the parameters driving the model limit its use to the conditions under which the parameters are selected. While general trends in shape alterations under defined boundary conditions are independent of the parameters used, the specific local amounts of material accretion or resorption predicted by each gradientless optimization-based shape adaptation model are parameter-specific.…”

Section: Theory Model Function and Prior Validationmentioning

confidence: 99%

Strength adaptations of the tibia bone for prescribed sets of isometric forces and joint angles

Florio

2017

SIMULATION

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The isometric exercise induced tibial bone strength adaptations due to various prescribed net resultant forces generated by a leg arranged with specified hip, knee, and ankle joint angles were examined using a computationally based bone shape adaptation model. With the leg straight, or the knee flexed at 90°, and the hip either neutral or flexed by 45°, a force was repeatedly generated at the toe either anteriorly, posteriorly, superiorly, or inferiorly, in paired sequences of these directions, or in a clockwise pattern of all four directions. Model-predicted individual muscle forces, amounts of cortical bone surface accretion or resorption, and the resulting changes in bone stress distributions were compared. Similarities between adaptations to specific combinations of joint angles and net resultant force directions were found to follow similarities in the bone stress distributions rather than in muscle activity. The ratio of standard deviation to the surface-averaged measure of local stress was a good predictor of potential improvement in overall stress state uniformity. With flexed knee and neutral hip, greater adaptive improvements in tibial surface stress uniformity were found than with both joints flexed. Flexed configurations caused greater changes and overall strength improvements than exercises performed with a straight leg. Regions of local tibial cortical thickening were identified for specific joint angles and singleload resultant force directions. Sequential series of loads were also identified to enhance these effects and mitigate concurrent thinning in other regions. The presented information can aid in the design and analysis of targeted muscle and bone strengthening exercises.

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“…Because of the mathematically lax nature of this gradientless type of optimization method, the model parameters, σ ref , α , and the stopping criteria are chosen by the model developer. Often, these parameters are based on experimental observations , the specific conditions studied , or to control model stability and mesh distortion . However, this makes the model suited only for the conditions under which the parameters were selected, requiring different parameter values not only for the study of different conditions but sometimes also for different portions of the design region, as multiple orders of magnitude variations in the stress measure are typical for large design regions, such as the surfaces of long bones .…”

Section: Model Developmentmentioning

confidence: 99%

Development and implementation of a coupled computational muscle force optimization bone shape adaptation modeling method

Florio

2015

Numer Methods Biomed Eng

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Improved methods to analyze and compare the muscle-based influences that drive bone strength adaptation can aid in the understanding of the wide array of experimental observations about the effectiveness of various mechanical countermeasures to losses in bone strength that result from age, disuse, and reduced gravity environments. The coupling of gradient-based and gradientless numerical optimization routines with finite element methods in this work results in a modeling technique that determines the individual magnitudes of the muscle forces acting in a multisegment musculoskeletal system and predicts the improvement in the stress state uniformity and, therefore, strength, of a targeted bone through simulated local cortical material accretion and resorption. With a performance-based stopping criteria, no experimentally based or system-based parameters, and designed to include the direct and indirect effects of muscles attached to the targeted bone as well as to its neighbors, shape and strength alterations resulting from a wide range of boundary conditions can be consistently quantified. As demonstrated in a representative parametric study, the developed technique effectively provides a clearer foundation for the study of the relationships between muscle forces and the induced changes in bone strength. Its use can lead to the better control of such adaptive phenomena.

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Shape optimization with the biological growth method: a parameter study

Abstract: The authors would like to express their thanks to Sage-Tübitak (Ankara), for supporting this study and permitting the use of their facilities.

Cited by 14 publications

References 7 publications

A Relative-Stress Based Method for Structural Shape Optimization

A Relative-Stress Based Method for Structural Shape Optimization

Strength adaptations of the tibia bone for prescribed sets of isometric forces and joint angles

Development and implementation of a coupled computational muscle force optimization bone shape adaptation modeling method

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