An analytical model for determining adhesive stress distributions within the adhesive-bonded single-lap composite joints was developed. ASTM D3165 ‘‘Strength Properties of Adhesives in Shear by Tension Loading of Single-Lap-Joint Laminated Assemblies’’ test specimen geometry was followed in the model derivation. In the model derivation, the composite adherends were assumed linear elastic while the adhesive was assumed elastic-perfectly plastic following von Mises yield criterion. Laminated Anisotropic Plate Theory was applied in the derivation of the governing equations of the bonded laminates. The adhesive was assumed to be very thin and the adhesive stresses are assumed constant through the bondline thickness. The entire coupled system of equations was determined through the kinematics relations and force equilibrium of the adhesive and the adherends. The overall system of governing equations was solved analytically with appropriate boundary conditions. Computer software Maple V was used as the solution tool. The developed stress model was verified with finite element analysis using ABAQUS by comparing the adhesive stress distributions.

We propose a new method for laminate stacking sequence optimization based on a two-level approximation and genetic algorithm (GA), and establish an optimization model including continuous size variables (thicknesses of plies) and discrete variables (0/1 variables that represent the existence of each ply). To solve this problem, a first-level approximate problem is constructed using the branched multipoint approximate (BMA) function. Since mixed-variables are involved in the first-level approximate problem, a new optimization strategy is introduced. The discrete variables are optimized through the GA. When calculating the fitness of each member in the population of GA, a second-level approximate problem that can be solved by the dual method is established to obtain the optimal thicknesses corresponding to the each given ply orientation sequence. The two-level approximation genetic algorithm optimization is performed starting from a ground laminate structure, which could include relatively arbitrarily discrete set of angles. The method is first applied to cylindrical laminate design examples to demonstrate its efficiency and accuracy compared with known methods. The capacity of the optimization strategy to solve more complex problems is then demonstrated using a design example. With the presented method, the stacking sequence in analytical tools can be directly taken as design variables and no intermediate variables need be adopted.

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A two-level multipoint approximation concept is proposed. Based upon the values and the first-order derivatives of the critical constraint functions at the points obtained in the procedure of optimization, explicit functions approximating the primal constraint functions have been created. The nonlinearities of the approximate functions are controlled to be near those of the constraint functions in their expansion domains. Based on the principle above, the first-levd sequence of explicitly approximate problems used to solve the primarily structural optimization problem are constructed. Each of them is approximated again by the second-level sequence of approximate problems, which are formed by using the linear Taylor series expansion and then solved efficiently with dual theory. Typical numerical examples including optimum design for trusses and frames are solved to illustrate the power of the present method. The computational results show that the method is very efficient and no intermediate/generalized design variable is required to be selected. It testifies to the adaptability and generality of the method for complex problems.

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