
φFEM, a finite element method on domains defined by levelsets: the Neumann boundary case
We extend a fictitious domaintype finite element method, called ϕFEM a...
read it

Finite elements for Helmholtz equations with a nonlocal boundary condition
Numerical resolution of exterior Helmholtz problems requires some approa...
read it

Trefftz Finite Elements on Curvilinear Polygons
We present a Trefftztype finite element method on meshes consisting of ...
read it

Geometry Mapping, Complete Pascal Scheme versus Standard Bilinear Approach
This paper presents a complete Pascal interpolation scheme for use in th...
read it

Cut finite element error estimates for a class of nonlinear elliptic PDEs
Motivated by many applications in complex domains with boundaries expose...
read it

Circumferential Crack Modeling of Thin Cylindrical Shells in Modal Deformation
An innovative technique, called conversion, is introduced to model circu...
read it

A Unified Finite Strain Theory for Membranes and Ropes
The finite strain theory is reformulated in the frame of the Tangential ...
read it
Generalization of a reduced Trefftz type approach
Summary This work presents variational concepts associated with reduced Trefftz type approaches and discusses the interrelationship between various concepts of the displacement, hybrid and Trefftz methods. The basic concept of the displacement version of the reduced Trefftz method operates on the natural boundary conditions enforced in an integral form whereas the stress version of the reduced Trefftz type approach operates on the essential boundary conditions enforced in an integral sense. The application of the method proposed in the framework of the finite element method is briefly outlined. The methods used by the reduced Trefftz type approach for enforcing conformity and interelement continuity between neighboured elements are also discussed. Comparisons with other known methods for the same purpose are performed. General strategy for developing finite elements of general geometric form such as quadrilateral elements with invariance properties is presented. The basic idea of this strategy consists in using the natural coordinate system only for defining the element geometry and performing the element integration in the biunit interval. For defining the approximation functions a local coordinate system defined from the directions of the covariant base vectors and the perpendicular contravariant base vectors computed in the geometric centre of the element is used. This strategy can also be used to implement other versions of finite elements and other forms of finite elements. Different numerical calculations and comparisons in the linear statics and kinetics are performed in order to assess the convergence and the numerical performance of finite elements developed by applying the reduced Trefftz type approach.
READ FULL TEXT
Comments
There are no comments yet.