The presented paper is focused on the stress-strain analysis of the restored tooth. For this problem computational modelling was chosen using the finite element method. The tooth is modelled from dentin and dental enamel with a class II cavity. The size of the dental cavity is considered in three sizes and three shapes. For restoration two types of filling materials were used. A physiological model of the tooth was created as well. Force was prescribed on the occlusal surface of the tooth. The analysis of results shows that from the different filling materials, and their interaction with the dental tissues, amalgam is from a mechanical aspect the best material for the restored tooth in the molar segment. and Obsahuje seznam literatury
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.
We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value contains three unknown fields: a gradient field discretized by Raviart-Thomas elements, Lagrange multipliers field discretized by piecewise constant functions and a scalar parameter β. The minimization of the majorant value is realized by an alternate minimization algorithm, whose convergence is discussed. Numerical results validate two estimates, the energy estimate bounding the error of approximation in the energy norm by the difference of energies of discrete and exact solutions and the majorant estimate bounding the difference of energies of discrete and exact solutions by the value of the functional majorant.