**4. Emerging areas and recommendations**

Sigmund and Maute [11] drawn a good framework on the classification of methodologies, and they pointed an important spot that differences between topology

**81**

**Author details**

Marmara University Engineering Faculty, Istanbul, Turkey

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: akentli@marmara.edu.tr

provided the original work is properly cited.

Aykut Kentli

*Topology Optimization Applications on Engineering Structures*

optimization approaches become small and an approach evolves into the other by the time such as evolutionary methods are converging towards discrete SIMP schemes. However, this trend has gone forward using hybrid approaches rather than becoming similar techniques to keep all the approaches having their advantages and limitations. There are many studies using hybrid methodologies given before under different headings, but there is still room for new applications. Especially from evolutionary algorithms perspective, using new optimization algorithms will enable

Another important area to work on is how uncertainties are handled. Topology optimization of small sized systems brings researchers to the position where small changes should be taken into account as todays' technology is covering nano-sized systems beyond MEMS. In any case when changes are formed either because of manufacturing errors or that applied loads has caused comparatively large deformations on members, it will not be possible to use precise geometry and crisp size values in the optimization stage. So, handling uncertainties such as using fuzzy

Lastly, another rapidly growing area at the last decade is rapid prototyping. Even though there are abundant studies in literature (over a hundred studies could be easily found [173]), new algorithms on the application of BESO, handling composite/functionally graded materials, and considering support and structure in the

In addition to the aforementioned emerging areas, researchers are encouraged to study (1) to develop the efficiency of standard methods; (2) to construct new benchmarking problems; (3) to consider several constraints rather than buckling, stress, or displacement of such natural frequency; (4) to adapt meshes to nonlinear geometries with a more accurate way; (5) to develop GUIs to help researcher to observe/interfere the optimization stage; and (6) to implement new meshless

*DOI: http://dx.doi.org/10.5772/intechopen.90474*

to improve methodologies advanced up to now.

systems is still an open field to study.

meantime are the promising areas to study.

methods rather than EFG such as peridynamics.

#### *Topology Optimization Applications on Engineering Structures DOI: http://dx.doi.org/10.5772/intechopen.90474*

*Truss and Frames - Recent Advances and New Perspectives*

**3.6 Meshless methods**

Shu et al. [143] used LSM in the design of coupled structural-acoustic system with a focus on interior noise reduction. Suresh and Takalloozadeh [144] used LSM considering stress constraints. Xia et al. [145] used LSM to maximize the simple or repeated first eigenvalue of structure vibration. Xia et al. [146] built a strict 0–1 model considering stress to be minimized. Xia et al. [147] optimized both structure and support using traction free and Dirichlet boundaries separately. Yamasaki et al. [148] proposed a method combined application of boundary element mesh with LSM. Zhu and Zhang [149] used LSM without re-initialization for the optimization of compliant mechanisms. Zhu et al. [150] combined projection Lagrangian method with piecewise constant level-set functions to manage the optimization for elliptic boundary value problems. Zhu et al. [151] used LSM to optimize hinge-free compliant mechanisms with multiple outputs. Zhu and Zhang [152] developed an accelerated level-set evolution algorithm by adding an extra energy function to be able to optimize the distributed compliant mechanisms. Zhu et al. [153] developed a new LSM to manage multiobjective optimization of hinge-free compliant mechanisms.

Lin et al. [154] generated a method mimicking leaf venation and using element-free Galerkin method to design heat conduction channels. Wang and Luo [155] proposed a meshless Galerkin level-set method using compactly supported radial basis functions to construct the meshless shape functions. Cui et al. [156] proposed a new method based on SIMP and using EFG method for multi-material optimization problems. Zhao [157] developed a new approach based on Pareto frontier solutions using EFG method. He et al. [158] combined density variable approach with EFG to optimize geometrically nonlinear structures. Evgrafov [159] proposed a method based on SIMP combined with Petrov-Galerkin methods based on minimizing the squared residual. Khan et al. [160] used EFG with LSM and also implemented sensitivity analysis. Gong et al. [161] developed a new method, particle moving, based on EFG considering density gradient and combined it with SIMP. Hur et al. [162] used a Spline-based meshfree method where nonuniform rational B-spline functions are used to smooth trimmed boundaries. Ren et al. [163] used a method combination of EFG and SIMP to design a two-material micro-compliant mechanism under stress constraints. Zhang et al. [164] applied a combined method of SIMP and direct coupling method of FE and EFG methods to decrease computational cost of meshless methods. Ai and Gao [165] integrated a parametric level-set method with a meshless method based on compactly supported radial basis functions. Wang et al. [166] applied EFG to the design of large displacement compliant mechanisms having geometrical nonlinearity. Yang et al. [167] applied EFG to the design of continuum structures under displacement constraints. Kefal et al. [38] combined BESO with a new meshless method peridynamics. Zheng et al. [168] used a combination of SIMP and EFG to optimize free vibrating continuum structures. Zhang et al. [169] used a directly coupled FE and EFG to optimize nonlinear hyperelastic structures. Luo et al. [36] used dual-level point-wise density approximation with EFG. Wu et al. [170] improved EFG by adding moving least squares approximation. Zheng et al. [171] used EFG to optimize geometrically nonlinear continuum structures. Zhao [172] combined BESO with EFG.

**80**

**4. Emerging areas and recommendations**

Sigmund and Maute [11] drawn a good framework on the classification of methodologies, and they pointed an important spot that differences between topology

optimization approaches become small and an approach evolves into the other by the time such as evolutionary methods are converging towards discrete SIMP schemes. However, this trend has gone forward using hybrid approaches rather than becoming similar techniques to keep all the approaches having their advantages and limitations. There are many studies using hybrid methodologies given before under different headings, but there is still room for new applications. Especially from evolutionary algorithms perspective, using new optimization algorithms will enable to improve methodologies advanced up to now.

Another important area to work on is how uncertainties are handled. Topology optimization of small sized systems brings researchers to the position where small changes should be taken into account as todays' technology is covering nano-sized systems beyond MEMS. In any case when changes are formed either because of manufacturing errors or that applied loads has caused comparatively large deformations on members, it will not be possible to use precise geometry and crisp size values in the optimization stage. So, handling uncertainties such as using fuzzy systems is still an open field to study.

Lastly, another rapidly growing area at the last decade is rapid prototyping. Even though there are abundant studies in literature (over a hundred studies could be easily found [173]), new algorithms on the application of BESO, handling composite/functionally graded materials, and considering support and structure in the meantime are the promising areas to study.

In addition to the aforementioned emerging areas, researchers are encouraged to study (1) to develop the efficiency of standard methods; (2) to construct new benchmarking problems; (3) to consider several constraints rather than buckling, stress, or displacement of such natural frequency; (4) to adapt meshes to nonlinear geometries with a more accurate way; (5) to develop GUIs to help researcher to observe/interfere the optimization stage; and (6) to implement new meshless methods rather than EFG such as peridynamics.
