Numerical Modeling and Software for Determining the Static and Linkage Parameters of Growing Bodies in the Process of Nonstationary Additive Heat and Mass Transfer

Abstract

Currently, methods of three-dimensional printing of products from polymer, metal and ceramic materials are widely used. Layer-by-layer synthesis technologies make it possible to obtain high-quality products with sufficiently high mechanical characteristics close to those realized using traditional technological processes. A related problem is solved, including calculating the temperature in the product and the operation area surrounding it in a flat setting based on two different approaches. For a layer-by-layer extensible body, the unsteady heat conduction problem is stated. At each step, the height of the computational region increases due to the filling of a new layer of powder. One time step of the calculation is determined by the interval between two consecutive passes of the laser. The temperature distribution found at each step is used as the initial conditions for the calculations at the next step. The temperature field obtained as a result of solving the problem that is implemented in the product in question with a step of 1000 (after applying and melting 1000 layers) is further compared with the solution of the quasi-stationary problem for the finite dimensions product. Using the example of the simple geometry taken, it is shown that a quasi-stationary solution can provide a satisfactory estimate of the macroscopic thermal state of the growing product.

Numerical Analysis of Deformation Characteristics of Elastic Inhomogeneous Rotational Shells at Arbitrary Displacements and Rotation Angles

“…where µ 1(k) and µ 2,(k) are the smallest and largest eigenvalues for the corresponding difference operators in equations ( 22); a ε,(k) and a t,(k) are the correction factors close to unity. The time step ∆t for the whole difference scheme is determined from the condition of the form (28):…”