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Internal Loadings in Structural Members: Problem Solving01:28

Internal Loadings in Structural Members: Problem Solving

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When designing or analyzing a structural member, it is important to consider the internal loadings developed within the member. These internal loadings include normal force, shear force, and bending moment. Engineers can ensure that the structural member can support the applied external forces by calculating these internal loadings.
To illustrate this, let's consider a beam OC of 5 kN, inclined at an angle of 53.13° with the horizontal and supported at both ends. Determine the internal...
1.4K
Unsymmetric Loading of Thin-Walled Members: Problem Solving01:07

Unsymmetric Loading of Thin-Walled Members: Problem Solving

157
The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
Next, calculate the moments of...
157
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

295
A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by...
295
Shear and Bending Moment Diagram: Problem Solving01:24

Shear and Bending Moment Diagram: Problem Solving

1.8K
When analyzing a beam supporting concentrated loads and a distributed load, drawing the shear and bending moment diagrams is essential. These diagrams help understand the internal forces and moments acting on the beam, which is crucial for designing safe and efficient structures. Follow these steps to create the shear and bending moment diagrams:
Draw a Free-Body Diagram: Start by drawing a free-body diagram of the entire beam, including the concentrated loads, distributed load, and reaction...
1.8K
Space Trusses: Problem Solving01:29

Space Trusses: Problem Solving

634
A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
Consider a tripod consisting of a tetrahedral space truss with a ball-and-socket joint at C. Suppose the height and lengths of the horizontal and vertical...
634
Problem Solving in Statics01:28

Problem Solving in Statics

776
Problem-solving in statics is a crucial aspect of engineering and physics that involves resolving issues associated with bodies in a state of equilibrium. In most cases, problem-solving requires several steps to achieve an accurate result. These steps are crucial to ensuring that the solution is accurate and practical.
The physical situation and mathematical modeling must be considered; however, it is challenging to represent all physical situations using mathematical modeling. With the help of...
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Related Experiment Video

Updated: Sep 4, 2025

Design and Optimization Strategies of a High-Performance Vented Box
14:23

Design and Optimization Strategies of a High-Performance Vented Box

Published on: June 9, 2023

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Application of QUBO solver using black-box optimization to structural design for resonance avoidance.

Tadayoshi Matsumori1, Masato Taki2, Tadashi Kadowaki2

  • 1DENSO CORPORATION, 500-1, Minamiyama, Komenoki-cho, Nisshin, Aichi, 470-0111, Japan. tadayoshi.matsumori.j7b@jp.denso.com.

Scientific Reports
|July 15, 2022
PubMed
Summary

This study introduces a new black-box optimization method for designing printed circuit boards to avoid resonance. The approach efficiently optimizes structures, improving calculation speed and success rates for finding optimal designs.

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Area of Science:

  • Engineering
  • Computational Science
  • Materials Science

Background:

  • Quadratic Unconstrained Binary Optimization (QUBO) solvers offer potential for structural design optimization, including resonance avoidance.
  • Current limitations in QUBO applications stem from the complexity of problem transformation.
  • Black-box optimization (BBO) methods, utilizing machine learning and Bayesian approaches, have emerged to address these challenges in combinatorial optimization.

Purpose of the Study:

  • To propose a novel black-box optimization (BBO) method for designing printed circuit boards (PCBs) to prevent resonance.
  • To formulate the PCB design problem as maximizing natural frequency while minimizing mounting points.
  • To overcome the challenge of approximating natural frequency for QUBO formulation within a BBO framework.

Main Methods:

  • A factorization machine-based black-box optimization (BBO) method was developed for PCB resonance avoidance.
  • The natural frequency, a key challenge for QUBO, was approximated using a quadratic model.
  • Probabilistic neighbor generation and model updating were employed for efficient approximation around optimal solutions.

Main Results:

  • The proposed BBO method successfully identified optimal mounting point positions for PCBs.
  • The method demonstrated a shorter calculation time compared to conventional BBO techniques.
  • A higher success probability in finding optimal solutions was achieved with the proposed approach.

Conclusions:

  • The developed BBO method offers an effective solution for PCB resonance avoidance.
  • This research enhances the applicability of QUBO solvers in structural design.
  • The findings suggest broader potential for QUBO in various structural engineering applications.