Ryszard Korycki

SENSITIVITY ANALYSIS AND OPTIMAL DESIGN FOR STEADY CONDUCTION PROBLEM WITH RADIATIVE HEAT TRANSFER

ABSTRACT A steady heat conduction problem is considered, that is described by the heat conduction equation and the thermal boundary conditions (i.e., Dirichlet, Neumann, Henkel, and radiation conditions on the external boundary, and radiation condition on the hole boundary). An arbitrary behavioral functional is defined and its first-order sensitivity is derived using both the direct and the adjoint approaches. The shape optimization problem is next formulated and two optimization functionals are discussed. The simple numerical example is presented.

Second-Order Sensitivities with Respect to Shape of Loaded and Supported Structural Boundaries∗

Abstract For an arbitrary stress, strain, and displacement functional, second-order sensitivities with respect to varying structural shape are discussed. It is assumed that the external boundary of a structure can undergo shape modification described by a set of shape design parameters. Second derivatives of an arbitrary functional with respect to these parameters are obtained, using the mixed approach in which both the direct and adjoint first-order solutions are used. The general results are particularized for the case of the complementary energy of a structure.

Simulations of Heat Transport Phenomena in a Three-Dimensional Model of Knitted Fabric

Abstract The main goal of the current work is to analyse the three-dimensional approach for modelling knitted fabric structures for future analysis of physical properties and thermal phenomena. The introduced model assumes some simplification of morphology. First, fibres in knitted fabrics are described as monofilaments characterized by isotropic thermal properties. The current form of the considered knitted fabric is determined by morphological properties of the used monofilament and simplification of the stitch shape. This simplification was based on a particular technology for the knitting process that introduces both geometric parameters and physical material properties. Detailed descriptions of heat transfer phenomena can also be considered. A sensitivity analysis of the temperature field with respect to selected structural parameters was also performed.

Thickness Optimisation of Textiles Subjected to Heat and Mass Transport during Ironing

Abstract Let us next analyse the coupled problem during ironing of textiles, that is, the heat is transported with mass whereas the mass transport with heat is negligible. It is necessary to define both physical and mathematical models. Introducing two-phase system of mass sorption by fibres, the transport equations are introduced and accompanied by the set of boundary and initial conditions. Optimisation of material thickness during ironing is gradient oriented. The first-order sensitivity of an arbitrary objective functional is analysed and included in optimisation procedure. Numerical example is the thickness optimisation of different textile materials in ironing device.

Thickness Optimisation of Sealed Seams in Respect of Insulating Properties

The main goal is to determine the optimal thickness of material layers in seams in respect of their insulating properties. The impact of structure on heat insulation and moisture resistance is also described. The insulation was analysed for different types of sealed seams which are typically used to connect the different parts of clothing. The coupled heat and mass transport problem is defined by the transport equations and a set of boundary and initial conditions. Based on the variational approach, we introduce the typical objective functionals and the optimality conditions. The problem was solved using the finite element method at the analysis stage and sensitivity approach at the synthesis stage.

Optimisation of Pad Thicknesses in Ironing Machines During Coupled Heat and Mass Transport

*Department of Design, Shoes and Clothing Technology, University of Technology and Humanities in Radom, Radom, Poland Abstract The main goal of the paper is to determine the physical and mathematical models of coupled heat and mass transport within pads during ironing as well as optimize the pads thicknesses. Introducing the Fick’s diffusion in fibers, heat and mass transport equations are formulated and accompanied by a set of boundary and initial conditions. Optimization of thickness is gradient oriented, the necessary objective functionals are analyzed. Numerical examples of optimization concerning the pads thickness are presented.

Local Optimization of Bonnet Thickness in Global Heat Balance of Neonate

Global heat transport for an neonate body is determined by means of heat balance with the term describing evaporation. The heat storage rate is the unbalanced difference between the metabolic heat production and various heat loss mechanisms within all body parts. The most sensitive portion is the head, which forces local optimization of the bonnet thickness. The local problem is described by differential heat and mass transport equations and the set of conditions. The changeable covering area of the bonnet can equalise the global heat balance and prevent hyperthermia or hypothermia.

Shape Determination of Elastica Subjected to Bending by Means of Displacements

Free folding of flat textiles can be determined using elastica for the same shape, loads and folding conditions across the product. The paper presents a general theory concerning shape determination of coplanar elastica subjected to static bending by means of displacements. The displacements are described by the coordinates of points of initially unbending elastica and the loads imposed. The physical behavior of elastica is described using some simplifications by both physical and mathematical models. The mathematical model can be discussed using a solution of six nonlinear differential equations with appropriate boundary conditions. Three relationships are the equations of equilibrium, and the other describes the displacements along the particular axis, the change in curvature and the physical law.

Numerical Optimisation of Thickness of Composite Bonnet for Neonates

Abstract Head is the most sensitive body part of neonate. Head that is considerably uncovered causes the significant heat and moisture loss from the skin to the surrounding areas. The main goal is to optimise the thickness of a multilayer composite textile bonnet to secure the optimal skin parameters. Problem is solved using both sensitivity analysis and material derivative concept. An arbitrary objective functional is introduced, its first-order sensitivity is formulated by means of a direct approach. Numerical application is the thickness optimisation of a composite bonnet made of different textile materials.