The phrase "analyses based on numerical" is not complete and lacks clarity in written English.
It can be used when discussing research or findings that rely on numerical data, but it needs to be followed by a noun to be fully effective.
Example: "The analyses based on numerical data revealed significant trends in consumer behavior."
Alternatives: "studies grounded in numerical" or "evaluations derived from numerical".
For comparison purposes, results from two-dimensional (2D) analyses based on the numerical limit analysis methods and the conventional limit equilibrium method (LEM) are also discussed.
In this paper, systematic analyses, based on a numerical approach introduced in a companion paper, are performed for the shoring systems installed to support applied loads during construction.
The conducted analyses based on the numerical homogenization procedure employ a spatial periodically arranged in a square array representative volume element and the finite element method.
In order to verify the contribution of the porous column and nanoPS layers to the efficient photo-acoustic emission, numerical analyses based on the one-dimensional heat transfer model were performed [13, 20].
Engineering analyses based on the results of numerical simulation enable shortening the duration and reducing the costs of the development and tests of equipment models or prototypes.
Although the model has found some utility in elucidating the role of inelasticity in stress re-distribution around strain concentrating features, we find that, in some instances, finite element analyses based on this model exhibit numerical convergence problems.
Several numerical analyses based on finite element method of the component were performed using the commercial software ABAQUS.
Both experimental tests (based on the Design of Experiment approach) and numerical analyses (based on the Finite Elements Method) have been carried out to obtain the proposed results.
Numerical analyses, based on Finite Element Method (FEM), were performed in order to model a cohesive law of the adhesive interface.
Analytical and numerical analyses based on the Mathieu and modified Mathieu equations are performed to investigate the interplaying effects of pulsatile pressure gradients and the slip lengths on the electroosmotic flow.
