Data Fitting with Least Squares in Solid Mechanics

When analyzing materials in solid mechanics, raw experimental data from tension tests can be noisy and difficult to interpret. Understanding how to mathematically fit this data is essential for extracting reliable material properties like Young's modulus and yield strength. This course provides a clear, step-by-step guide to applying the least squares method to mechanical engineering data, turning raw test measurements into precise material models. You will transition from raw experimental data points to confident, mathematically sound material characterizations. By understanding the underlying optimization principles, you will be able to filter out experimental noise and make highly accurate engineering predictions. What you'll learn: - Understand the core mathematical theory of least squares regression and curve fitting - Analyze experimental tension test data to identify elastic and plastic deformation regions - Calculate Young's modulus by fitting linear models to stress-strain data - Apply non-linear fitting techniques to model complex material behaviors - Evaluate the quality of your fit using statistical metrics like residuals and R-squared - Use modern Python libraries such as NumPy and SciPy to automate the data-fitting process This course begins with fundamental definitions of stress, strain, and optimization theory before moving into practical mathematical formulations and code-based implementation. You will work through structured written explanations, step-by-step mathematical derivations, and clean code examples designed to solidify your understanding. This course is designed for engineering students, laboratory technicians, and beginning researchers in civil, mechanical, or aerospace engineering who want to master data analysis for solid mechanics. No advanced background in optimization is required, though a basic familiarity with algebra and introductory programming concepts is helpful. Master the mathematics of material testing and start fitting your experimental data with precision today.