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In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
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Traverse angle computations are a critical component of surveying, used to compute the internal angles within a closed traverse. A traverse consists of a series of connected lines forming a closed loop, often used for land boundary delineation or mapping. Calculating the internal angles ensures accuracy in the traverse geometry and is essential for checking survey data integrity.The process begins with known azimuths and bearings of the traverse sides. Internal angles at each vertex are...
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Bending of Material: Problem Solving01:09

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In this lesson, determine the ratio of the maximum bending moments applied to two metal pipes, given that both pipes can withstand a maximum stress of 100 MPa. Both pipes have an outer radius of 1.8 cm. Pipe A has an inner radius of 1.5 cm, and Pipe B has an inner radius of 1 cm. The ratio of the maximum bending moment applied to two metallic pipes, each with a different inner and outer radius, is determined by considering their dimensions. The inner radius of the first pipe is 1.5 cm, and for...
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The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and...
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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.
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Updated: Sep 12, 2025

Designing CAD/CAM Surgical Guides for Maxillary Reconstruction Using an In-house Approach
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Engineering oriented shape optimization of GHT-Bézier developable surfaces using a meta heuristic approach with

Samia BiBi1, Md Yushalify Misro1,2, Muhammad Abbas3

  • 1School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Gelugor, Pulau Pinang, Malaysia.

Scientific Reports
|August 5, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces the Improved-Grey Wolf Optimization (I-GWO) technique for optimizing GHT-Bézier developable surfaces in CAD/CAM. The method effectively refines shape control parameters for enhanced surface design and manufacturing.

Keywords:
Developability degreeDevelopable surfacesGHT-Bézier curveI-GWO algorithmShape parameters

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Area of Science:

  • Engineering and CAD/CAM
  • Computational Geometry
  • Optimization Techniques

Background:

  • Optimization is crucial for designing free-form surfaces and manufactured products.
  • Real-world engineering challenges often employ optimization with objective functions.

Purpose of the Study:

  • To present the shape optimization of GHT-Bézier developable surfaces using the Improved-Grey Wolf Optimization (I-GWO) technique.
  • To find optimal shape control parameters for improved surface design.

Main Methods:

  • Utilized the Improved-Grey Wolf Optimization (I-GWO) meta-heuristic algorithm.
  • Formulated optimization models based on arc length (AL), minimum energy (En), and curvature variation energy (CVEn) of dual and interpolation curves.
  • Employed an iterative process to determine optimal shape control parameters.

Main Results:

  • Successfully applied the I-GWO technique to optimize GHT-Bézier developable surfaces.
  • The construction of these surfaces was formulated using optimal shape parameters derived from I-GWO.
  • The developability degree of the resulting surfaces was determined.

Conclusions:

  • The I-GWO technique provides an effective method for the shape optimization of GHT-Bézier developable surfaces.
  • The proposed approach enhances surface design and manufacturing processes in engineering.
  • Demonstrated practical applications and the effectiveness of the developed method.