Mechanics of Solids and Shells: Theories and Approximations

Snap-through Behavior and Button Design

“…1, the snap-through problem is a typical topic in solid mechanics. Many past researches (1)(2)(3)(4)(5) have studied this problem. The snap-through behavior has been applied to the button design ( Fig.…”

Explicit finite deformation analysis of isogeometric membranes

“…A key feature of membrane structures is their high slenderness ratio and their ability to resist significant membrane stress whilst minimising their weight [1]. Due to their extreme efficiency in addressing particular types of environments and achieving outstanding functionalities, engineered membrane structures are also used for a wide range of applications such as building fabric structures (e.g.…”

“…airbag, parachute, landing system of Mars Rover) [2,3]. The large slenderness associated with membrane structures means that the structural bending stiffness is generally very small and even negligible [1,4]. In the latter case, stress states characterised by negative principal components are not admissible.…”

“…In the latter case, stress states characterised by negative principal components are not admissible. As a result, large deformations such as ballooning, local wrinkling or folding are produced to minimise the potential energy of the system [5] The mechanical response of these very thin shell/membrane structures is more naturally described by the Kirchhoff-Love shell theory [6][7][8] incorporating membrane strains and change in curvature due to bending rather than full three-dimensional constitutive theories or Reissner-Mindlin shell theory [1] which include transverse shear stress. The accurate modelling of such thin structures under large deflection, rotation and strain is essential for understanding the mechanics of biological membranes (here, membrane refers to the biological meaning) [9][10][11] which is one of the motivations for the present study.…”

“…It is estimated that about 80% of overall analysis time is devoted to mesh generation in a number of industries such aerospace or automotive [19]. An important point for the computational analysis of Kirchhoff-Love shells is that 1 C continuity is required between elements [6,7,20,21] as curvature is a function of the second derivatives of the displacement, which is rather difficult to achieve for free-form geometries when using polynomial basis functions [6]. These polynomial shape functions, when applicable, introduce undesirably high order polynomials with inherent disadvantages such as oscillations in the discrete solution and costly numerical integration (see, e.g.…”