Abstract

A monolithic approach to fluid-structure interactions based on the space-time finite element method is presented. It is applied to investigate stress states in silos during centric and eccentric discharges. Using the continuum approach, the silo-shell is modelled as an elastic solid, whereas the bulk material is described by a model for viscoplastic compressible fluids. Between the fluid and sol-id, advanced slip boundary conditions incorporating friction are taken into account. In order to solve the governing equations of the multi-field problem, the weighted residual method is ap-plied, which is discretized by time-discontinuous space-time finite elements. Within the simulta-neous solution procedure for the coupled problem, the kinematics of both solid and fluid is de-scribed by velocities as primary variables. A mesh-moving scheme based on a pseudo-structure adapts the coordinates of the nodes in the fluid domain to the structural deformation. The non-linear system of equations composed of physical unknowns and velocities of the fluid mesh is solved iteratively applying the Newton-Raphson scheme. For the investigation of stress states inside thin-walled structures, isoparametric quadratic finite elements are applied. Whereas in structural elements uniform ansatz functions are used for both the velocities and the stresses, the fluid is discretized by quadratic Taylor-Hood elements, ap-proximating the density respectively the pressure with linear functions. The position of the free surface between bulk material and air above is given implicitly using a signed distance function, which is approximated by quadratic polynomials as well due to con-sistency. The motion of the free surface is described by the level-set-method. According to the mechanics the level-set-equation is numerically solved using a Galerkin method. Hence the mo-tion of the bulk material is not being strongly affected by the air above, a single-phase level-set-method is applied leading to meshes which in general are composed of active and inactive finite elements. Intersected elements are evaluated precisely using integration rules based on tessella-tion. A pde-based extrapolation of the velocity-field ensures an accurate transport of the free sur-face.