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What is meant in these excerpts?

What is meant in these excerpts?

What is meant in these excerpts?

In the first picture χ_α is defined as "the perturbation field", and in the second its "element test fields". I am trying to make sense of it, but I dont see what is meant by it nor what it does, could someone give me their interpretation and maybe it would make more sense?

RE: What is meant in these excerpts?

C. R. Thomsen, F. Wang, O. Sigmund, Buckling strength topology optimization of 2d periodic materials based on linearized bifurcation analysis, Computer Methods in Applied Mechanics and Engineering 339 (2018) 115–136.

F. Wang, O. Sigmund, Numerical investigation of stiffness and buckling response of simple and optimized infill structures, Structural and Multidisciplinary Optimization 61 (2020) 2629–2639.

F. Wang, O. Sigmund, Extreme 3D architected isotropic materials with tunable stiffness and buckling strength (page 3-4, equation 2)

RE: What is meant in these excerpts?

What do you guys think is meant by solving for perturbation field?

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