An integrated equivalent stiffness model is developed to describe a grid structure with or without laminate skins. The in-plane bending and shear of ribs are included without introducing any extra degree of freedom so that Mindlin's plate theory can still be adopted. As a result, the model can be directly incorporated with the existing FEM technique and take advantage of commercial codes. The proposed model is demonstrated to be efficient and reasonably accurate. If high precision is required, the equivalent stiffness model can be incorporated with the exact FEM modeling to obtain a refined stress analysis. Hygrothermal behavior and local buckling are also taken into account. Using the model as a tool, the performance of composite grid structures can be compared to traditional laminates, sandwich plates and metal grid structures. A method of optimum design is established to design a grid structure with or without laminated skins. Multiple loads and multiple failure mechanisms are considered. Discrete design is also included. Furthermore, the method can be easily incorporated with FEM to perform structural optimization. The optimization code is demonstrated to be a very powerful design tool. Finally, a user-friendly computer code is developed to perform the above tasks.

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Closed-form expressions of three-dimensional effective moduli of symmetric laminates, which are based on the assumption of constant in-plane strains and constant interlaminar stresses through the thickness, had been proposed by Chou and Carleone (1972) and later re-proposed by Sun and Li (1988). This article modified the effective interlaminar shear moduli to account for the effect of stacking sequence by assuming the parabolic distribution of interlaminar shear stresses through the thickness. In this article, the effective three-dimensional moduli are also re-presented in such forms that it could be seen that several particular forms of the rule of mixture apply for individual stiffness or compliance components. As a result, four stiffness invariants and one compliance invariant are developed. The invariance is helpful in checking the reliability of measurements. The effective moduli predicted by this article are found to be in good agreement with the experimental data measured by ultrasonic methods.