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Statically Indeterminate Problem Solving01:16

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Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
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Design Consideration01:22

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Designing a structure involves a series of considerations, primarily the material's ultimate strength, calculated through tests that measure changes under increased force until the material reaches its breaking point or limit. The ultimate load, where the material breaks, is divided by its original cross-sectional area, resulting in the ultimate normal stress or strength. The ultimate shearing stress is another significant factor taken into account.
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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented...
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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
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A Parameter Reduction-Based Decision-Making Method with Interval-Valued Neutrosophic Soft Sets for the Selection of

Honghao Zhang1,2, Lingyu Wang1, Danqi Wang3

  • 1Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), School of Mechanical Engineering, Shandong University, Jinan 250061, China.

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Selecting optimal bio-inspired thin-wall structures for safety applications is simplified. This study introduces a novel method using interval-valued neutrosophic soft sets (IVNS-SOFT) to effectively weigh criteria and select the best structure.

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Area of Science:

  • Engineering
  • Materials Science
  • Biomimetics

Background:

  • Bio-inspired thin-wall structures offer superior mechanical properties for transportation and aerospace safety.
  • Selecting optimal structures based on multiple attributes and engineering preferences is challenging.

Purpose of the Study:

  • To develop a robust method for selecting bio-inspired thin-wall structures.
  • To address limitations in subjective evaluations and redundant parameters in decision-making.

Main Methods:

  • Proposed a parameter reduction-based indifference threshold-based attribute ratio analysis method under an interval-valued neutrosophic soft set (IVNS-SOFT).
  • Developed an IVNS-SOFT-based multi-attributive border approximation area comparison (MABAC) method for optimal alternative selection.
  • Quantified uncertainty and handled inconsistent expert information.

Main Results:

  • The proposed IVNS-SOFT approach effectively determines the weight vector for evaluation indicators.
  • The IVNS-SOFT-MABAC method successfully identifies optimal bio-inspired thin-wall structures.
  • Demonstrated the method's validity and practicality through an application case study.

Conclusions:

  • The developed method provides an effective tool for selecting bio-inspired thin-wall structures.
  • The approach enhances decision-making by managing uncertainty and improving attribute weighting.