Cut finite element modeling of linear membranes

• We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus, i.e., with the equilibrium equations pointwise projected onto the tangent plane of the surface to create a pointwise planar problem in the tangential direction. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization of the membrane comes from a Galerkin method using the restriction of 3D basis functions (linear or trilinear) to the surface representing the membrane. In the case of coupling to 3D elasticity, we view the membrane as giving additional stiffness contributions to the standard stiffness matrix resulting from the discretization of the three-dimensional continuum.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Teknisk mekanik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Applied Mechanics (hsv//eng)

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datorteknik (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Engineering (hsv//eng)

Keyword

Cut finite element method

Membrane shell

Embedded membrane

Tangential derivative

LFOUR MC

1995

JOURNAL OF DIFFERENTIAL EQUATIONS

V119

P426 nsbo Peter

2015

FINITE ELEMENTS IN ANALYSIS AND DESIGN

V102-103

P1 rman E.

2015

ArXiv e-prints

Publication and Content Type

ref (subject category)

art (subject category)