This paper presents an improved generalized procedure for dealing with the stability of thin-walled beams under combined symmetric loads based on the energy method. The differential equations for the case of complex loading conditions were developed using an axis transformation matrix. The work caused by external loads was related to the work of internal forces to simplify the computational procedure. The thin-walled beam subjected to axial force [Formula: see text], bending moment [Formula: see text] at both ends, and concentrated load [Formula: see text] at midspan was studied. The case of a concentrated load [Formula: see text] replaced by a distributed load [Formula: see text] over partial beam length was also examined. The stability region boundary of the beam was derived by two approaches: one was to estimate an approximate angle of twist prior to determination of the deflection and the other was to do it in the reverse way. Numerical results reveal that the first approach yields less error than the second; however, the outcome obtained by the former was more cumbersome than the latter. Above all, both approaches provided feasible results and are useful for further applications dealing with the stability analysis of thin-walled beams.

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A new technique is described, used by the authors to automate the design process of the main drive of a new generation machine intended for industrial washing of fruits and vegetables. To solve the problem of multi-criteria design, the original approach is proposed that uses interconnected mathematical models describing the dynamic behavior, strength reliability and functional characteristics of the machine in a unified information space. The generalized mathematical model includes 12 controlled parameters, 16 functional constraints, and 3 quality criteria. A genetic algorithm was used to find the space of Pareto-optimal solutions. The situational approach was used to select the final rational solution from a set of solutions belonging to the Pareto-optimal domain. The rational design of option the washer found using the proposed approach is compared with the existing ones. The proposed design methodology can be recommended for the design of a wide range of similar mechanical structures.

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This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force [Formula: see text], bending moment [Formula: see text] and distributed load [Formula: see text] (or concentrated load [Formula: see text]) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.