Optimization is performed on two applications from woodmanufacturing, with the main focus on wood drying. As anintroductory study of optimization, the design of a modernracing ski is investigated. The skating ski, which is partlybuilt up by wood, is optimized against maximum stiffness withthe restriction of a limited upper weight.
Wood drying is treated as an optimization problem. The totaldrying time is minimized, at the same time as restrictions onmoisture content, stresses and deformations are considered. Theoutcome of the optimization is drying schedules which describethe environmental air dry temperature and relative humidity asa function of time. Design variables during optimization arethe length of the individual time steps and the air drytemperature and relative humidity connected to each time step.Convex approximation methods are used for optimization (the socalled MMA-method, Method of Moving Asymptotes). Necessarygradients are calculated with finite differences.
Optimization is performed with one- and two-dimensional (1Drespectively 2D) moisture transport models. In optimizationwith 1D analysis, moisture content and stresses are calculatedalong a line in the middle of the board, and with 2D analysisthe calculations are made in a numerical grid which covers thecross section of the board. In both cases, deformations arecalculated as the global cup deformation. All structuralcalculations are made with a FEM-program (FEM = Finite ElementMethod) where the whole cross section is modelled with onesingle element. The moisture calculations are made with aFEM-program in the 1D-case, and with a FD-program (FD = FiniteDifference) in the 2D-case. The transient solutions of thestructural and moisture problems are obtained with a timestepping procedure. It is assumed that the moisture problem canbe solved separately from the structural problem, i.e. that thestress and strain distribution during drying has no influenceon the moisture transport.
The wood material is modelled as an orthotropic materialwith main directions in the radial, tangential, andlongitudinal directions. Most material parameters vary with themain direction, the temperature and the moisture content. Thetotal strain rate in the structural calculation is assumed tobe the sum of the elastic strain rate, the moisture inducedstrain rate and the mechano-sorptive strain rate. It ispossible to vary the dimensions of the board and the growthring orientation (i.e. the pith position). In thetwo-dimensional model, it is also possible to simulatedifferent distributions of sapwood and heartwood in the crosssection.
Numerical examples are performed with both 1D and 2Danalysis. In the last example with 2D analysis, optimization isperformed as distributed computing with computers in anetwork.
The thesis shows that optimization methods work well forwood drying. Modern optimization routines offer powerful toolswhen constructing reliable drying schedules. The knowledgeobtained in this work can be used to refine existing dryingschedules, to develop schedules for new quality demands or tocreate schedules for drying kilns with improvedperformance.
Keywords:Optimization, wood drying, distributedcomputing, drying schedules, one-dimensional, two-dimensional,stresses, deformations, moisture content.
Institutionen för byggnader och installationer , 2000. , 42 p.