The paper concerns slackened systems, i.e. discrete deformable systems with gaps (clearances) at structural joints. The mathematical model of such systems coincides with a FEM-oriented approximation of locking-elastic-plastic bodies. The theory describes a relatively wide class of systems made of time-independent materials. The problem of slackened systems has been developed during the last decade. The work presents the current state of knowledge in this field.
The available methods and solutions of problems in discrete optimum structural design are reviewed. They are classified into the following categories: branch and bound methods, dual approach, enumeration methods, penalty function approach, simulated annealing and other methods. For the majority of problems, none of the methods is guaranteed to give the exact solution from the mathematical point of view. However, "good practical'' solutions can be obtained at an acceptable cost.
We look directly into the phase space of experimental or numerical data to derive nonlinear equations of motion. Our example is the dynamics of viscous droplets. While the smallest useful dimension of phase space turns out to be three, we apply methods to visualize four, five, six dimensions and more. These methods are Poincairé sections and condensation of variables. The resulting equations of motion are extremely simple but nevertheless realistic.
In this paper, information on a sheet metal forming simulation program based on flow approach is provided and comparisons between numerical and experimental results are presented. Elastic spring-back effects and residual stresses are predicted by means of a large-strain elasto-viscoplastic finite element model recently proposed for this class of problems involving large deformations and changes in geometry. A wide experimental program performed in a sheet stamping factory is shortly described. Tests included the deep drawing of circular and rectangular blanks with cylindrical and prismatic tools, respectively. Different die and punch roundings, lubrication conditions and blank holder forces have been considered. Different examples of application to 2D and 3D sheet stamping problems are presented and compared with available experimental results.
The paper presents a heuristic method of node renumbering for wavefront reduction of the coefficient matrix of a linear system of equilibrium equations obtained in Finite Element (FEM) or in Finite Difference (FDM) methods for regular rectangular domains. From among all the node renumbering techniques for the Banachiewicz-Cholesky triangular decomposition of an assembled matrix with a compact (the least sparse possible) profile, the method presented herein assures the best reduction of matrix wavefront and time of decomposition
A rectangular specimen consists of two kinds of grains. Each kind has a different thermal expansion coefficient. The grains are randomly distributed in J rows and K columns of the specimen. The temperature of the whole specimen is increased and produces internal strains. It is assumed that each grain interacts with its four neighbours. The interaction force is proportional to the relative displacement. If the relative displacement equals the extension due to thermal expansion, the force equals zero. The relaxation method of calculating the equilibrium strains is used. The average maximum strains are calculated for a large number of numerical experiments. The standard deviations are calculated.
A solution to plane and axisymmetric elasto-plastic contact problem with linear hardening of contacting bodies, taking into account microstructural features of the contact zone is presented. A new quadratic-isoparametric contact element involving the irreversible nature of friction is developed. An incremental constitutive friction law, analogous to the classical theory of plasticity, is used. Several numerical examples are considered. The influence of parameters defining the contact stiffness interface on the distribution of displacements and stresses on the contact surface is discussed.