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"The efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field. In contrast to existing texts on structural optimization, Introduction to Shape Optimization: Theory, Approximation, and Computation treats sizing and shape optimization in a comprehensive way, covering everything from mathematical theory (existence analysis, discretizations, and convergence analysis for discretized problems) through computational aspects (sensitivity analysis, numerical minimization methods) to industrial applications. Some of the applications included are contact stress minimization for elasto-plastic bodies, multidisciplinary optimization of an airfoil, and shape optimization of a dividing tube. By presenting sizing and shape optimization in an abstract way, the authors are able to use a unified approach in the mathematical analysis for a large class of optimization problems in various fields of physics."

"Mahalnya harga baja yang disebabkan oleh pandemi Covid-19 mengharuskan kita mencari cara agar produksi tetap berjalan. Salah satunya yaitu dengan optimasi, akan tetapi lamanya waktu optimasi menimbulkan masalah baru pada hal tersebut. Pada penelitian ini penulis mencoba melakukan optimasi pada struktur kapal dengan menggunakan persamaan Axial Stress dan Bending Stress. Penelitian ini dilakukan pada struktur plat geladak dengan 2 kondisi pembebanan yang berbeda, yaitu beban distribusi merata dan beban tarik. Pada penelitian ini didapatkan bahwa optimasi yang dilakukan dengan menggunakan persamaan axial stress lebih cepat 54% dibandingkan optimasi yang menggunakan persamaan bending stress. Selain itu, pada penelitian ini juga sukses menurunkan berat model sebesar 38% pada kondisi 1 dan sebesar 51% pada kondisi 2.

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The high price of steel caused by the Covid-19 pandemic requires us to find ways to keep production running. One of them is optimization, but the length of time for optimization creates new problems in this regard. In this study, the author tries to optimize the ship structure using the Axial Stress and Bending Stress equations. This research was conducted on the deck plate structure with 2 different loading conditions, namely uniform distribution load and tensile load. In this research, it was found that the optimization using the axial stress equation was 54% faster than the optimization using the bending stress equation. In addition, this study also succeeded in reducing the model weight by 38% in condition 1 and by 51% in condition 2 ."

"Manufaktur aditif, melalui perkembangan dan penyebarannya, telah memungkinkan kebebasan yang lebih besar dalam hal desain komponen dan kemudahan untuk menguji desain tersebut. Elemen umum yang digunakan dalam desain untuk manufaktur aditif adalah mengubah geometri padat menjadi bentuk berongga dengan struktur lattice internal untuk mempertahankan kekakuan dan kekuatan bentuk awal. Studi ini bertujuan untuk mengembangkan sebuah metode optimalisasi struktur lattice pada komponen yang dikenai beban, dengan tujuan meminimalisasi volume material yang digunakan serta stres yang dialami oleh komponen tersebut. FEA digunakan untuk menentukan kepadatan dari lattice pada area tertentu, menambahkan material ke area yang mengalami stres tinggi dan menguranginya pada area yang mengalami stres rendah. Kerangka ini diuji pada batang yang mengalami beban lentur. Perbandingan kemudian dilakukan dengan struktur lattice berbentuk seragam.

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Additive manufacturing has, through its development and proliferation, allowed for greater degrees of freedom when it comes to the design of components and ease at which to test said designs. A common element used in designing for additive manufacturing is turning a solid geometry into one that is hollow with an internal lattice structure to maintain stiffness and strength. This study aims to develop a method of optimizing the lattice structure of a component under load, aiming to minimize both volume of material used as well as stress experienced by the component. FEA is used to determine the relative density of the lattice at a given area, adding material to areas of high stress and removing it in areas of low stress. This framework is tested on a beam that is experiencing a bending load. A comparison is then made to a lattice structure of uniform shape."