Analytical Stress Calculation for Multi-Planar Objects
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Solution Overview
Problem
Classical contact mechanics formulas fail to provide accurate solutions for determining deformation and stress in objects with multiple planar surfaces under applied load, especially when edge surfaces affect internal stress and strain fields, as they assume a loaded object is an elastic half-space, leading to inaccuracies in mechanical components like rail-wheel systems and cutting tools.
Innovation Solution
An analytical method is developed to determine stress and strain fields by assigning and transforming loads on multiple planar surfaces into equivalent loads using a transformation matrix, allowing the application of classical half-space formulae to calculate induced stresses and strains, which are then used to predict mechanical failure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If classical contact mechanics formulas are used to determine stress and deformation, then the calculation process is simple, but the accuracy is poor because the formulas assume an elastic half-space model which does not account for edge surface effects
Solution Approach 1:
The patent divides the planar surface into multiple uniformly loaded sections, each with a defined center point. This segmentation allows the complex 3D stress distribution to be approximated by summing the effects of simpler uniform loads on each section, thereby improving accuracy while maintaining computational feasibility.
Solution Approach 2:
The patent introduces equivalent loads as an intermediary concept. Instead of directly solving the complex 3D boundary value problem, the method transforms the actual non-uniform loading into equivalent uniform loads that produce the same stress distribution. This intermediary transformation simplifies the calculation while preserving accuracy.
2Reliability
If the loaded object is modeled as an elastic half-space, then the analytical solution is straightforward, but the solution becomes inaccurate when edge surfaces significantly affect internal stress and strain fields
Solution Approach 1:
The patent applies different loading characteristics to different regions of the planar surface. By dividing the surface into multiple sections with distinct center points and applying uniform loads to each section, the method captures local variations in stress distribution that arise from edge surface effects, thereby improving reliability without requiring a completely complex geometric model.
3Productivity
If analytical methods are used to determine stress fields, then computational time is reduced, but the method cannot accurately handle objects with multiple planar surfaces under complex loading conditions
Solution Approach 1:
The patent applies uniform loads to each segmented section of the planar surface, which may be more loading than actually applied in the original problem. However, by carefully selecting the segmentation and load distribution, the method achieves accurate stress field determination while maintaining analytical efficiency. The excessive action is controlled to avoid unnecessary computational complexity.
Data Source
AI summary
An analytical method of determining the solution of an object with a plurality of planar surfaces under applied load includes the steps of assigning the load applied on each of the plurality of planar surfaces in the three dimensional directions respectively, determining the equivalent load applied on each of the plurality of planar surfaces in the three dimensional directions from the applied loads with the stress boundary conditions, and determining the stress and strain fields from the equivalent load applied on each of the plurality of planar surfaces.