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This paper presents a numerical procedure for the analysis of complex laminate structures. The procedure is based on the application of reduced stiffness of complex laminate. Introduction of reduced stiffness of composite facilitates both linear and nonlinear numerical integration, i.e. the tangential stiffness matrix is translated in the classical plate theory problem. The formulated numerical procedure was implemented in the program system KOMIPS. Special subroutine REDKRUT that calculates reduced stiffness of the laminate was written, and its application in numerical verification of experiments conducted on chairs was presented in (Nestorovic, 2010). At the end of this work, for 3D stress and strain analysis of veneer composites, recommendations were given for experimental determination of all nine independent material constants Ex, Ey, Ez, vxy, vxz, Gxy, Gxz, Gyz, fi ve of which were determined in the previous paper of the author (Nestorović, 2010)., Rad prikazuje numeričku proceduru za analizu struktura izrađenih od kompleksnih laminata. Postupak se temelji na primjeni reducirane krutosti komplesnog laminata. Uvođenjem reducirane krutosti kompozita numerička se integracija, kako linearne, tako i nelinearne, odnosno tangencijalne matrice krutosti, prevodi u problem klasične teorije ploča. Formulirana numerička procedura implementirana je u sklopu programskog paketa KOMIPS. Napisana je posebna subrutina REDKRUT, kojom se proračunavaju reducirane krutosti laminata, a njegova primjena u provjeri numeričkih eksperimenata provedenih na stolcima prikazana je u radu (Nestorovic, 2010.). Za 3-D analizu naprezanja i deformacija furnirskih kompozita na kraju ovog rada dane su preporuke za eksperimentalno određivanje svih devet neovisnih materijalnih konstanti: Ex, Ey, Ez, vxy, vxz, Gxy, Gxz, Gyz, od kojih je pet određeno u prethodnom autoričinu radu (Nestorović, 2010.).

This paper presents a numerical procedure for the analysis of complex laminate structures. The procedure is based on the application of reduced stiffness of complex laminate. Introduction of reduced stiffness of composite facilitates both linear and nonlinear numerical integration, i.e. the tangential stiffness matrix is translated in the classical plate theory problem. The formulated numerical procedure was implemented in the program system KOMIPS. Special subroutine REDKRUT that calculates reduced stiffness of the laminate was written, and its application in numerical verification of experiments conducted on chairs was presented in (Nestorovic, 2010). At the end of this work, for 3D stress and strain analysis of veneer composites, recommendations were given for experimental determination of all nine independent material constants Ex, Ey, Ez, vxy, vxz, Gxy, Gxz, Gyz, fi ve of which were determined in the previous paper of the author (Nestorović, 2010)., Rad prikazuje numeričku proceduru za analizu struktura izrađenih od kompleksnih laminata. Postupak se temelji na primjeni reducirane krutosti komplesnog laminata. Uvođenjem reducirane krutosti kompozita numerička se integracija, kako linearne, tako i nelinearne, odnosno tangencijalne matrice krutosti, prevodi u problem klasične teorije ploča. Formulirana numerička procedura implementirana je u sklopu programskog paketa KOMIPS. Napisana je posebna subrutina REDKRUT, kojom se proračunavaju reducirane krutosti laminata, a njegova primjena u provjeri numeričkih eksperimenata provedenih na stolcima prikazana je u radu (Nestorovic, 2010.). Za 3-D analizu naprezanja i deformacija furnirskih kompozita na kraju ovog rada dane su preporuke za eksperimentalno određivanje svih devet neovisnih materijalnih konstanti: Ex, Ey, Ez, vxy, vxz, Gxy, Gxz, Gyz, od kojih je pet određeno u prethodnom autoričinu radu (Nestorović, 2010.).

Experimental determination of the elastic constants of orthotropic composite materials and their bearing capacity (strength) for furniture intended for sitting, and numerical verification of the experiment results by analysing with the final elements, was performed on the basis of the theory of elasticity of orthotropic and anisotropic composite materials. The requisite and sufficient material constants were determined in the experiments: moduli of elasticity and Poisson’s coefficients (longitudinal and tangential) and skate modulus for plain stress. These constants, calculated by 3D measurements of deformation, are sufficient for determining the constitutive matrix of the lamina, and for reducing stiffness of the composite irrespective of the thickness of the layers, fibre orientation and choice of material. Experiments were conducted for the stiffness, shear and flexing of uniformly and complexly layered beech veneer sheets, while for new materials experiments for stiffness and shear in a uniform orientation were sufficient. Analysis of stiffness and deformations were conducted layer by layer, as well as by reduced volume stiffness for multilayered orthotropic shells of chair systems by a method of final elements by application of a composite final element, where combined reduced membrane matrices and flexing matrices are used. Numerical verification of the experiments, including systems of furniture intended for sitting – chairs – was conducted using the KOMIPS software system, which contains in its library a composite final element of the sheet. Experiments with chairs were performed with the aim of determining the stiffness of such systems, and they were confirmed by analytical results and measurement of the real movements on selected models. The results of research provide the design, re-design, construction and determination of the dimensions of not just chairs, but also of any other girder or surface system based on laminates., Na temelju teorije elastičnosti ortotropnih i anizotropnih kompozitnih materijala eksperimentalno su određene elastične konstante i nosivost (čvrstoća) ortotropnih kompozitnih materijala za namještaj za sjedenje te je provedena numerička potvrda eksperimentalnih rezultata analizom uz primjenu konačnih elemenata. U radu su određene ove konstante materijala: modul elastičnosti i Poissonov koeficijent (uzdužni i tangencijalni) te klizni modul za naprezanje u ravnini. Te konstante, izračunane na temelju 3D mjerenja deformacija, dovoljne su za određivanje konstitutivnih matrica uslojenog drva i za smanjenje krutosti kompozita, bez obzira na debljinu slojeva, orijentaciju vlakanaca i odabrani materijal. Na uzorcima od uslojenih podjednakih bukovih furnira provedena su eksperimentalna mjerenja krutosti, čvrstoće smicanja i savijanja, iako su za nove materijale dovoljna samo ispitivanja krutosti i smicajne čvrstoće u istom smjeru. Analiza krutosti i deformacija napravljena je sloj po sloj, kao i za smanjenu volumnu krutost višeslojnih ortotropnih ploča za stolce, metodom konačnih elemenata, uz primjenu kompozitnoga konačnog elementa, pri čemu se primijenjuje kombinacija reduciranih membranskih matrica i matrica savijanja. Numerička potvrda rezultata eksperimenta, uključujući sustav namještaja za sjedenje – stolce – provedena je primjenom softvera KOMIPS, koji u svojoj zbirci ima kompozitni konačni element za ploče. Eksperiment sa stolcima proveden je radi određivanja krutosti takvog sustava te je potvrđen analitičkim rezultatima i mjerenjima stvarnih pomaka na izabranim modelima. Rezultati istraživanja omogućuju dizajn, redizajn, konstruiranje i određivanje dimenzija ne samo stolaca nego i drugih nosača ili površina utemeljenih na uslojenom drvu.