Analysis and Improvement of Virtual Work Criteria for Structure Optimization
An improvement of virtual work criteria for structure optimization is presented to overcome the shortcomings caused by the neglect of dead weight and inertial load of structure in solution of criteria equations. Deduction of criteria equations is analyzed to prove that the shortcomings lead to the error of structure optimization. Therefore, new criteria equations are formulated using the displacement representation of algebraic sum and matrices. According to the characteristics of the improved criteria equations, an improved Aitken algorithm is applied to solve the equations in order to implement the complete automatization of iterative solution for structure optimization. The algorithm is proved to be an accelerated iterative method, and its convergence order is estimated. The feasibility of improved criteria equations and the merits of improved Aitken algorithm are demonstrated by an illustrative example showing five-bar truss. The results show that the improvement of virtual work criteria provides a structure optimization method for precision machine.
Optimising structures using the principle of virtual work
This paper presents a method for optimising structures with a given geometry and loading based on the principle of virtual work. The Virtual Work Optimisation Method, or VWOM, that was developed minimises the mass of the structure while meeting building code strength requirements, and flexibility (or deflection) criteria. The optimisation can be readily constrained by grouping together members with the same sectional properties. The VWOM automates most of the design process, obviating the requirement of experience and expertise in stiffening a structure. 
Three case studies were conducted using the VWOM: (i) the benchmark optimisation ten-member truss; (ii) a truss frame designed by professional engineers; and (iii) a 24-storey frame. The results of the VWOM were compared with published or available solutions. The VWOM produced structures that were 0,9 to 15,1% lighter than those produced by the methods used in the comparisons. If every member was allowed to have its own sectional properties, the VWOM found even lighter structures (by as much as 19,5%). The VWOM is less computationally expensive than the comparison methods, requiring two or three orders of magnitude fewer iterations to converge to the solution.
New approach to vision-based BGA package inspection
Ball grid array (BGA) techniques have developed very fast due to the advantages of more I/O ports, small size, and so on. In this paper, a vision-based algorithm for BGA package inspection is proposed to accurately estimate center and diameters of solder-balls of BGA packages, so that defects of BGA packages, such as missing or extra balls, oversize or undersize balls, over-height or under-height balls, and pitch can be detected for ensuring the quality of BGA packages.