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The governing equations for plates of transversely isotropic material are solved by the well-known Galerkin procedure.
Two types of problems, supersonic external flow over fractal-like immersed body and subsonic internal flow through a porous material are solved using the multi-GPU DSMC solver.
The 12 scalar ordinary differential equations governing the free vibration behavior of cylindrical helical springs made of an anisotropic material are solved simultaneously by the transfer matrix method.
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The nonlinearity of the model, which mainly comes from the use of amorphous alloy as core material, was solved by parameter identification and in-depth mathematical analysis.
Stochastic finite element equations for rigid – poroplastic materials are solved for the first two probabilistic moments.
Thereafter, 3-D elasto-static equations for orthotropic materials are solved for bending analysis of laminated plates using two different approaches.
Bending problem of simply supported microbeams made of functionally graded materials is solved by Navier's solution procedure.
Governing equations with material-geometric non-linearities are solved by implementing iterative Newton-Raphson method to trace large-deformation non-linear equilibrium path.
Material constitutive response and internal energy are carried on discrete points (material points), while the governing equations are solved on an overlying grid.
Full time-dependent solutions of the equations governing cake growth are solved, using representative material properties based upon experimental results.
Numerous examples on material layout determination for compliant mechanisms are solved with flexibility-stiffness and flexibility-strength multi-criteria formulations to illustrate the essence of this paper.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com