Identifying inclusions in a non-uniform thermally conductive plate under external flows and internal heat sources using topological optimization

Abstract

We propose applying topological optimization methods based on measuring temperature and heat fluxes to estimate the thermal conductivity of inhomogeneous thermally conductive plates and determine the shape and location of foreign inclusions. Examples of plates subjected to external heat fluxes and heat sources are considered. The solutions are obtained with the help of the finite element method combined with the method of moving asymptotes. The results show that identification accuracy depends on the defined boundary conditions, the source intensity value, heat fluxes, temperature distribution and the shape of the inclusions. For the problem of 18 circular inclusions under different heat fluxes, identification accuracy increases with increasing source intensity values.

A New Approach to Identifying an Arbitrary Number of Inclusions, Their Geometry and Location in the Structure Using Topological Optimization

“…We intend to examine some examples of challenges of identifying an arbitrary number and planning inclusions, their geometry and their location in a plate, under the influence of temperature and thermal flows, using topological optimization. Let us consider an isotropic flat body in the form of a thin plate occupying the area We write the classical differential heat equation [40] for the temperature field T inside the area…”

“…The body was under the action of both the temperature at the boundary B T (the Dirichlet (or first type) boundary condition) and the heat flux at the boundary B q (the Neumann (or second type) boundary condition). The temperature field T inside V satisfies the heat conduction equation [40] k∆T = 0, in V(x, y, z),…”

“…where k 1 , k 2 -are thermal conductivity coefficients in volumes V m , respectively, and p ≥ 1 is a penalty factor for the SIMP method. The goal function was defined as follows [40]:…”

“…Numerical tests to indicate the effectiveness of the developed approach were performed. Krysko et al [40][41][42][43] proposed the application of topological optimization methods based on temperature and heat flux measurements. The effects on the optimal topology of the composite in the presence of two competing materials were investigated, in addition to the optimality criteria, using linear weight functions.…”

Topological Optimization of Interconnection of Multilayer Composite Structures

“…Mesh dependency, which arises from the fact that a finer mesh allows for sharper optimal designs, can be mitigated by increasing the number of partitions. The authors of this work addressed this issue in their studies on the optimization of structures [24,25,35,36] as well as the identification of holes/inclusions [37,38].…”