Economic-design optimization of cross laminated timber plates with ribs

An economic-design optimization of cross-laminated timber (CLT) plate with stiffening ribs is presented. For the structural analysis, an enhanced assumed strain (EAS) solid finite element is used. It behaves well for thin plates (with no shear locking) and delivers reasonable approximations for the transverse shear stresses in layered composites. Eurocodes 5 (EC5) are followed in defining the optimization constraints, which include deflections, stresses and fundamental eigenfrequency. The gradient optimization is performed. Analytical expressions for sensitivities are obtained by an automatic differentiation tool. The result is an economic timber plate configuration that complies with the EC5 requirements. Numerical examples are presented in order to illustrate the approach.