Fourier Integral Transformation Method for Solving Two Dimensional Elasticity Problems in Plane Strain Using Love Stress Functions
Bibliographic record
Abstract
The Fourier integral method was used in this work to determine the stress fields in a two dimensional (2D) elastic soil mass of semi-infinite extent subject to line and strip loads of uniform intensity acting on the boundary. The two dimensional plane strain problem was formulated using stress-based method. The Fourier integral was used to transform the biharmonic stress compatibility equation to a fourth order linear ordinary differential equation (ODE) in terms of the stress function. The ODE was solved subject to the boundedness condition to obtain the bounded stress function. Cartesian stress components were obtained using the Love stress functions. Application of the stress boundary conditions for the case of line load of uniform intensity and the cases of uniformly distributed load on a strip of finite width gave the respective unknown constants of the Love stress functions; and hence the complete determination of the Cartesian stress components for the two cases considered. Inversion of the Fourier integral expressions obtained for the normal and shear stresses in the Fourier parameter gave respective expressions for the normal and shear stress fields for line and finite strip loads of finite width in the physical domain variables. The results obtained agreed with the results from previous studies which used displacement based methods.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".