Minimization of the stress concentration in Formed Parts through Non-Parametric Optimization


  • Salam. O Dahe Al Furat Al Awsat Technical University
  • Badr Kamoon Al-Furat Al-Awsat Technical University, Iraq
  • Hamzah Kadhim Al-Furat Al-Awsat Technical University, Iraq



Numerical Analysis, Stiffness, Structure topology, Simulation, ABAQUS


Parametric and non-parametric are the main optimization methods that are used in various industrial fields. In non-parametric optimization, the process of manipulating the node locations (shape optimization) or removing mass without changing the node locations (topology optimization) is adopted to achieve a desired objective. This structural optimization is formulated as a non-parametric problem, and for analysis purposes, ABAQUS/CAE software is adopted for this approach. Manufacturing process like forming is always linked with stress concentration, especially in the sharp ends and variable cross sections like holes and fillets. The problems of representation and finding the optimal and better structural design of some known quantities such as reactions, loads and masses is not easy. A large deflection may be induced in a structure when experiencing severe mechanical loads. In this work, the numerical method has been presented to investigate a method for optimization of formed parts geometry. Numerical examination confirmed that high-stress concentrations are generated in many places. Material distribution is highly influenced by nonlinearity and the new layout will result in intermediate densities. In such cases, the nonlinear elasticity like nonlinear strain must be considered. As a result, the non-parametric optimization can offer good design flexibility to use the existing model with ease of setup and without the need for parameterization. It can provide a conceptual design that can reduce the structure's weight to the maximum extent in the early design stage. This work is going to optimize the design of the formed plates by reducing the volume while maximizing its stiffness. As a recommendation, in order to provide an attractive approach with suitable levels of structural performance, the combination of both optimization methods is the short way to achieve this aim.


Musaddiq Abdil Khaliq Maleh Al-Ali. “Stress minimization of artificial bone using Non-Parametric Optimization”. Doctorate dissertation. Graduate School of Engineering Hiroshima University Japan 2018.

Hayoung Chunga, Oded Amirb, H. Alicia Kimc,d. “Level-set topology optimization considering nonlinear thermoelasticity”. Computer Methods in Applied Mechanics and Engineering, April 2020. Volume 361, 1, 112735.

Luca Furbatto, Giovanni Di Lorenzo and Claus B.W. Pedersen Luca Furbatto and Giovanni Di Lorenzo. Optimization in the Abaqus Environment Using TOSCA. Abaqus Users’ Conference. 2009.

M. Shimoda1, J. Tsuji2 & H. Azegami3 “.Non-parametric shape optimization method for thin-walled structures under strength criterion”. WIT Transactions on The Built Environment, 2019.Volume 91, DOI:10.2495/OP070171.

Georgi Chakmakov, Serafim Chatzimoisiadis, Dassault Systemes, Bulgaria, Beta CAE. Application of Non-Parametric Sizing Optimization for Car Body Parts Using Simulia Tosca Structure and Ansa. 6th Beta Cae International Conference, Greece. 2019.

Bogdan Szybiński. “Parametric and Topological Optimization of Different Designs of Flat Ends in Pressure Vessels”. Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 26-30 July 2015. Institute of Machine Design, Cracow University of Technology, Kraków, Poland.

Iandiorio, D Milani, and P Salvini. Shape optimization of 2D beam-structures to obtain the uniform strength. IOP Conf. Series: Materials Science and Engineering. (2023), 1275, 012030..

Vahid Keshavarzzadeh, Robert M.Kirby, Akil Narayan. “Parametric topology optimization with multiresolution finite element models”. 10 July 2019.DOI:10.1002/nme.6063.

Peter Gangl. Multi-objective free-form shape optimization of a synchronous reluctance machine. The international journal for computation and mathematics in electrical and electronic engineering Vol. 41 No. 5, 2022 pp. 1849-1864 Emerald Publishing Limited 0332-1649.

V.V. Chedrik, S.A. Tuktarov Central Aerohydrodynamic Institute (TsAGI), Zhukovsky, Russia. “Stress-Based Topology Optimization With Using Global-Local Approach”. (2018).

Roman Sartorti, Torsten Möcker, Benedikt Kriegesmann. Claus B.W. Pedersen. On non-parametric fatigue optimization. Int J Numer Methods Eng. 2023. ;124:1168–1192.

Sumit Jain1, Preety Mor2, Rajat Gupta3 and Pardeep Raman4. “The Parametric Optimization of Friction Stir Welding Process on Aluminum Alloy 6082-T6”. Int. J. Engg. Res. & Sci. & Tech. May 2015 © 2015 IJERST. ISSN 2319-5991 Vol. 4, No. 2,

Kishan Anand1, Anadi Misra. Topology Optimization and Structural Analysis of Simple Column and Short Pressurized Beams Using Optimality Criterion Approach in Ansys. International Research Journal of Engineering and Technology (IRJET). 2015.Volume: 02 Issue: 03 | June-

Evangelos Tyflopoulos, and Martin Steinert. Topology and Parametric Optimization-Based Design Processes for Lightweight Structures. Appl. Sci. 2020, 10, 4496; doi:10.3390/app10134496.

]15] Tae-Joong Yu. Topology Optimization under Stress Constraints. Master Thesis. 2003. University Of Florida University of Florida

D. Vlah , R. Žavbi and N. Vukašinović. Evaluation of Topology Optimization and Generative Design Tools as Support for Conceptual Design. 2020. International Design Conference – Design

Liang Xia, Li Zhang, Qi Xia, Tielin Shi. Stress-based topology optimization using bi-directional evolutionary structural optimization method. Computer Methods in Applied Mechanics and Engineering May 2018, Volume 333, Pages 356-370.

Altair Engineering, Inc. Practical Aspects of Structural Optimization with Altair OptiStruct. 2021.

Manyu Xiao, Jun Ma, Dongcheng Lu, Balaji Raghavan and Weihong Zhang. Stress-constrained topology optimization using approximate reanalysis with on-the-fly reduced order modeling. (2022), Advanced Modeling and Simulation in Engineering Sciences 9:17

Steffen Johnsen, Structural Topology Optimization Basic Theory, Methods and Applications. Master Thesis. Norwegian University of Science and Technology. 2013.

H. Mizhir Magid, S. Sulaiman, M. K. A. M. Ariffin and B. T. H. T. Baharudin. Stress analysis of forward aluminum extrusion process using finite element method. Materials Research Innovations 2014 VOL 18 SUPPL 2 S2-611. DOI 10.1179/1432891714Z.000000000626

Mu-Tsang Chena, and Ronald Harichandran. Statistics of the von Mises stress response for structures subjected to random excitations. (1998). ANSYS Inc., 275 Technology Dr., Canonsburg, PA 15317, USA. Shock and Vibration 5, 13–21.




How to Cite

Dahe, Salam. O, Badr Kamoon, and Hamzah Kadhim Hasan. 2023. “Minimization of the Stress Concentration in Formed Parts through Non-Parametric Optimization”. Metallurgical and Materials Engineering 29 (4).



Materials, Industrial, and Manufacturing Engineering