# Optimizing Support Locations in the Roof–Column Structural System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Optimal Column Locations

#### 2.1. Problem Definition

#### 2.2. Problem Statement

#### 2.3. Optimization Algorithm

## 3. Controlling Optimization Tendency

#### 3.1. Initial Discrete Candidates

#### 3.2. Roof–Column Relative Stiffness

#### 3.3. Filtering Scheme

## 4. Numerical Analysis

#### 4.1. Method

^{3}, respectively. The optimization solver considered all three improved techniques introduced in Section 3.

#### 4.2. Optimization Results

#### 4.3. Result Validation

## 5. Extended Designs

#### 5.1. Eye-Shaped Roof

#### 5.2. Bean-Shaped Roof

#### 5.3. Pavilion with Bean-Shaped Roof

#### 5.4. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Designing columns under a flat roof using optimization. Subfigures in top row represent initial setup, including flat roof with (

**a**) a continuous design domain, (

**b**) 3 × 3 discrete design domain, and (

**c**) 8 × 8 discrete design domain. Subfigures in second row represent optimization result obtained using (

**d**) bidirectional evolutionary structural optimization (BESO) topology method and (

**e**,

**f**) proposed new optimization method.

**Figure 2.**Designing column locations under a flat roof using (

**a**) 8 × 8 and (

**b**) 6 × 6 candidate columns.

**Figure 3.**Controlling optimization tendency with filter utilization. (

**a**) Intermediate state of optimization process. Optimization result generated (

**b**) without a filter and (

**c**) with a filter.

**Figure 5.**Finding 8 optimal column locations under a square roof. (

**a**) Three-dimensional illustration of candidate columns. Optimization results of ${t}_{s}$ = (

**b**) 0.2 and (

**c**) 0.3.

**Figure 6.**Manual test results of square-roof example with 8 columns arranged in (

**a**) ring and (

**b**) random configurations. (

**c**) Summary of comparison compliance.

**Figure 7.**Designing column locations under eye-shaped roof. (

**a**) Design domain. (

**b**) Optimization result. (

**c**) Manual results.

**Figure 8.**Designing column locations under bean-shaped roof. (

**a**) Design domain. (

**b**) Optimization result. (

**c**) Manual results.

**Figure 9.**Design of pavilion with bean-shaped roof. (

**a**) Roof–column structural system. (

**b**) Installation of curved panels. (

**c**) Intermediate optimization results.

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**MDPI and ACS Style**

Meng, X.; Lee, T.-U.; Xiong, Y.; Huang, X.; Xie, Y.M. Optimizing Support Locations in the Roof–Column Structural System. *Appl. Sci.* **2021**, *11*, 2775.
https://doi.org/10.3390/app11062775

**AMA Style**

Meng X, Lee T-U, Xiong Y, Huang X, Xie YM. Optimizing Support Locations in the Roof–Column Structural System. *Applied Sciences*. 2021; 11(6):2775.
https://doi.org/10.3390/app11062775

**Chicago/Turabian Style**

Meng, Xianchuan, Ting-Uei Lee, Yulin Xiong, Xiaodong Huang, and Yi Min Xie. 2021. "Optimizing Support Locations in the Roof–Column Structural System" *Applied Sciences* 11, no. 6: 2775.
https://doi.org/10.3390/app11062775