scholarly journals Integral Criterion of the Non-uniformity of Stress Distribution for the Topology Optimization of 2D-Models

2021 ◽  
Vol 24 (1) ◽  
pp. 65-74
Author(s):  
Ihor V. Yanchevskyi ◽  
◽  
Volodymyr F. Kryshtal ◽  

The emergence of new technologies for the production of structural elements gives impetus to the development of new technologies for their design, in particular with the involvement of a topology optimization method. The most common algorithm for designing topologically optimal structures is focused on reducing their elastic flexibility at a given volume of material. However, a closer to the engineering design approach is the minimization of the volume of a structural element while limiting the resulting mechanical stresses. In contrast to the classical algorithms of this approach, which limit the values of stresses at certain points, this paper develops an alternative criterion: the formation of the image of a structural element is based on minimizing the integral parameter of stress distribution non-uniformity. The developed algorithm is based on the method of proportional topology optimization, and when mechanical stresses are calculated, the classical relations of the finite element method are used. The above parameter can be interpreted as the ratio of the deviation of the values, ordered in ascending order, of equivalent von Mises stresses in the finite elements of a calculation model from their linear approximation to the corresponding mean value. The search for the optimal result is carried out for the full range of possible values of the averaged "density" of the calculation area, which is associated with a decrease in the amount of input data. The proposed integrated strength criterion provides better uniformity of the optimized topology, allows us to smooth the effect of the local peak values of mechanical stresses, determining a single optimization result that is resistant to calculation errors. The algorithm is implemented in the MatLab software environment for two-dimensional models. The efficiency of the approach is tested on the optimization of a classical beam (mbb-beam), a cantilever beam, and an L-shaped beam. A comparative analysis of the obtained results with those available in the literature is given. It is shown that in the absence of constraint on the average value of the density of a finite element model, the proposed criterion gives a ″less dense″ optimization result compared to the classical one (approximately 40%), while the values of "contrast index" are quite close.

Author(s):  
Yang Liu ◽  
Bingpeng Chen ◽  
Chenyu Wang ◽  
Hao Chen ◽  
Aobo Zhang ◽  
...  

Metal block augmentation, which is used for the treatment of tibial bone defects in total knee arthroplasty, with high stiffness will cause significant alteration in stress distribution, and its solid structure is not suitable for osseointegration. This study aimed to design a porous block to reduce weight, promote bone ingrowth, and improve its biomechanical performance. The metal block augmentation technique was applied to finite element models of tibial bone defects. Minimum compliance topology optimization subject to volume fraction combined with the porous architecture was adopted to redesign the block. Biomechanical changes compared with the original block were analyzed by finite element analysis. The stress distribution of the block and proximal tibia was recorded. The strain energy density of the proximal tibia was obtained. The newly designed block realized 40% weight reduction. The maximum stress in the optimized block decreased by 11.6% when compared with the solid one. The maximum stress of the proximal tibia in the optimized group increased by 18.6%. The stress of the anterior, medial, and posterior parts of the proximal medial tibia in the optimized group was significantly greater than that in the original group (all p < 0.05). The optimized block could effectively improve the biomechanical performance between the block and the bone. The presented method might provide a reference for the design of customized three-dimensional printed prostheses.


2014 ◽  
Vol 915-916 ◽  
pp. 240-243
Author(s):  
Sheng Bin Wu ◽  
Xiao Bao Liu

Aimed at the layout of inner stiffeners in excavator's boom, this paper puts forward an optimization method for the layout of box structure 's inner stiffeners and layout topology optimizes based on Evolutionary Structural Optimization (ESO). Analyzed the boom with the finite element method under the bucket digging condition, the results show that the inner stiffeners obtained by this method can improve the stress concentration phenomenon and the high stress distribution areas. The practices demonstrated the proposed method is effective and feasible.


2021 ◽  
Vol 332 ◽  
pp. 01015
Author(s):  
Szymon Imiłkowski ◽  
Stepan Kovalyshyn ◽  
Karolina Karolewska ◽  
Bogdan Ligaj ◽  
Mateusz Wirwicki

The aim of the article was to carry out FEM strength tests for four proposed by the authors geometry of the intraoral implant. Change of their geometrical features to find the most optimal distribution of reduced stresses. The article presents various geometries of the new dental implant. Strength tests were performed using the finite element method (FEM). The results of the tests were analyzed and their assessment was made for which of the solutions of the new geometry the stress distribution is the most optimal. Detailed results of the analyzes for a given model are shown and new solutions in the construction of the implant are proposed.


2011 ◽  
Vol 39 (4) ◽  
pp. 223-244 ◽  
Author(s):  
Y. Nakajima

Abstract The tire technology related with the computational mechanics is reviewed from the standpoint of yesterday, today, and tomorrow. Yesterday: A finite element method was developed in the 1950s as a tool of computational mechanics. In the tire manufacturers, finite element analysis (FEA) was started applying to a tire analysis in the beginning of 1970s and this was much earlier than the vehicle industry, electric industry, and others. The main reason was that construction and configurations of a tire were so complicated that analytical approach could not solve many problems related with tire mechanics. Since commercial software was not so popular in 1970s, in-house axisymmetric codes were developed for three kinds of application such as stress/strain, heat conduction, and modal analysis. Since FEA could make the stress/strain visible in a tire, the application area was mainly tire durability. Today: combining FEA with optimization techniques, the tire design procedure is drastically changed in side wall shape, tire crown shape, pitch variation, tire pattern, etc. So the computational mechanics becomes an indispensable tool for tire industry. Furthermore, an insight to improve tire performance is obtained from the optimized solution and the new technologies were created from the insight. Then, FEA is applied to various areas such as hydroplaning and snow traction based on the formulation of fluid–tire interaction. Since the computational mechanics enables us to see what we could not see, new tire patterns were developed by seeing the streamline in tire contact area and shear stress in snow in traction.Tomorrow: The computational mechanics will be applied in multidisciplinary areas and nano-scale areas to create new technologies. The environmental subjects will be more important such as rolling resistance, noise and wear.


1986 ◽  
Vol 14 (2) ◽  
pp. 125-136 ◽  
Author(s):  
Y. Nakajima ◽  
J. Padovan

Abstract This paper extends the finite element simulation scheme to handle the problem of tires undergoing sliding (skidding) impact into obstructions. Since the inertial characteristics are handled by the algorithm developed, the full range of operating environments can be accommodated. This includes the treatment of impacts with holes and bumps of arbitrary geometry.


2021 ◽  
Vol 1067 (1) ◽  
pp. 012141
Author(s):  
Muhsin J. Jweeg ◽  
H. A. Hamzah ◽  
Muhannad Al-Waily ◽  
Mohsin Abdullah Al-Shammari

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