Temperature Dependent Green's Function Calculation for Thermal Stress
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Solution Overview
Problem
Existing Green's function calculations do not accurately account for changes in physical properties of materials due to temperature changes, leading to inaccuracies in thermal stress value calculations.
Innovation Solution
A temperature-dependent Green's function is calculated using a weight function that considers changes in material properties, incorporating a material temperature change information input unit and separate units for steady and transient state thermal stress calculations, with weight functions designed as ratios or polynomial functions based on temperature changes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional Green's function is used for thermal stress calculation, then calculation simplicity is maintained, but measurement precision deteriorates because temperature-dependent material property changes are not reflected
Solution Approach 1:
The patent applies parameter changes by modifying the Green's function to be temperature-dependent, specifically by introducing a temperature-dependent elastic coefficient E(T) and thermal expansion coefficient α(T). The weight function W(T,τ) is designed to capture these parameter variations, transforming the traditional constant-parameter Green's function into a variable-parameter model that accurately reflects material property changes with temperature.
Solution Approach 2:
The weight function W(T,τ) serves as an intermediary element that bridges the traditional Green's function and the temperature-dependent material properties. It mediates between the temperature history φ(τ) and the thermal stress calculation, incorporating the effects of varying elastic and thermal expansion coefficients without requiring complete reformulation of the underlying mathematical framework.
2Measurement precision
If temperature-dependent material property changes are incorporated, then thermal stress calculation accuracy improves, but calculation complexity increases
Solution Approach 1:
The patent introduces dynamics by making the Green's function adaptive to changing temperature conditions. The weight function W(T,τ) dynamically adjusts the contribution of different temperature history segments based on the current temperature T and previous temperature τ, allowing the calculation model to automatically adapt to varying thermal conditions without manual intervention.
Solution Approach 2:
The patent applies preliminary action by pre-defining the weight function W(T,τ) and its relationship with temperature-dependent material properties. The functional form of the weight function and its connection to E(T) and α(T) are established in advance, allowing the system to handle temperature variations during operation without requiring real-time derivation or complex on-the-fly calculations.
Data Source
AI summary
Disclosed are an apparatus and a method for calculating a temperature dependent Green's function using an appropriate weight function. The apparatus includes a material temperature change information input unit inputting change information of a material temperature; and a temperature dependent Green's function calculation unit receiving the change information of the material temperature through the material temperature change information input unit, calculating a temperature dependent Green's function using a weight function, and outputting the calculated result. According to aspects of embodiments, accuracy in the calculation of a thermal stress value can be improved by designing the weight function such that changes in physical properties of a material that change according to temperature changes are considered.