A FINITE-ELEMENT ANALYSIS OF MULTI-LAYERED ORTHOTROPIC MEMBRANES WITH APPLICATION TO FABRIC SUPPORTED OIL PAINTINGS

A finite element formulation is developed for the analysis of multi-layered, orthotropic membranes, under the action of in-plane loading and with particular application to fabric supported oil paintings.; The formulation considers multi-layering of materials having significantly different elastic properties, but assumes that no inter-layer slip occurs and that orthotropic considerations are restricted to the case where the principal directions of orthotropy coincide with the coordinate directions. Variable humidity conditions and tension cracking can be considered.; The finite element formulation is developed using a rectangular linear-edge-displacement element, divided into nine equal subregions. An iterative procedure is utilized to consider cracking, whereby the original configuration is assumed uncracked and equivalent corrective nodal forces are applied. Subsequent analyses allow for previously cracked elements by modification of the overall structure stiffness matrix. A computer program to accurately represent the formulation is developed and validated by the consideration of a number of simplified trial problems.; In order to demonstrate the use of the program in the study of the effects of environmental and human actions on fabric supported oil paintings, some typical influences are studied. Using current data on the physical properties and dimensions of typical component materials, the displacements, stress distribution and extent of tension cracking within the component materials are evaluated. The computer program results give close agreement with cracking patterns observed on actual paintings.; It is concluded that, provided realistic material property data is available to accurately model the actual painting, the capability exists for the prediction and evaluation of the specific crack inducing stresses resulting from environmental and human actions.