Finite Element Method Linear Static And Dynamic Finite Element Analysis

By E. Kaestner. 2016

2,616 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/894a0f17789df56eee7e595cf90d1f9393332533

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Citations in the corpus

Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems (2021, methodology): “Moreover, the construction of PDE-informed graph convolutional network (GCN) structure is inspired by finite element (FE) method [25, 26], which is another classic numerical discretization technique that possess many advantages for physics-informed learning.”
Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis (2014, methodology): “Following [27, 38], the complete degree of quadrature accuracy required to satisfy criterion (7) for full tensor-product basis functions can be determined by the relation (d+1)p− 2m.”
Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity (2019, background): “This presentation of the strong (S), weak (W) and Galerkin (G) form are standard, see [29].”
Self-sensing concrete enabled by nano-engineered cement-aggregate interfaces (2017, methodology): “All the calculations have been carried out in the regular bi-unit square domain and thereafter transferred into the real domain using iso-parametric formulation.(44,45) Galerkin’s approximation states that the test function can be chosen to be the same as the nodal shape function, which turns equati”
Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework (2014, methodology): “holds and the resulting interpolated basis systems Ai are orthonormal, where the basis vectors A h α can be chosen to simplify the imposition of boundary conditions or simply according to the lamina coordinate system proposed in [19].”
A nonlinear, transient finite element method for coupled solvent diffusion and large deformation of hydrogels (2015, methodology): “Thus a mixed finite element method with both displacement and pressure as the unknown fields must be employed (Hughes, 1987).”
Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements (2016, methodology): “Although using IGA in TO may achieve some distinguished advantages, it is more difficult to implement geometric constraints in isogeometric TO than that in FEM TO, since the mesh of the NURBS-based IGA is based on the tensor product patch that usually does not conform to the geometrically constraine”
An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valves (2014, unknown): “The standard Gaussian quadrature rules typically applied to finite elements [109] assume that a polynomial can accurately approximate the integrand, but this assumption is not true if the integrand is discontinuous.”
Multiscale isogeometric topology optimization for lattice materials (2017, methodology): “In IGA, the discrete equilibrium equation of a linear elasticity problem may be written in the form of the conventional FEM as [54]”
The multi-level hp-method for three-dimensional problems: Dynamically changing high-order mesh refinement with arbitrary hanging nodes (2016, methodology): “For the numerical approximation of the solution, the multi-level hp-approach is combined with the Newmark time-stepping scheme using 48 time steps [17, 18, 78].”