Field of the Invention
The present disclosure is related to modeling and analysis tools for design and selection of weight-optimized structural members subject to load-bearing forces.
Background Information
Compressed thin wall structural members (“thin wall structures”) are well suited for a variety of applications ranging from construction projects to mechanical equipment and machinery design that require low weight, high strength and high stability and flexibility.
The basic principles of thin wall structural design optimization that have important practical significance for solving the inverse problem of structural mechanics are described in F. R. Shanley's textbook, Weight And Strength Analysis In Aircraft Design. In this work, problems of thin wall tubular column optimization and problems of designing a plate and tubular shell affected by the bending moment are solved; the issue of optimal installation of reinforcement plates (stringers and ribs) is addressed. These examples describe approaches to solving multi-parameter optimization problems based on use of fundamental principles of plates and bars structural theories applied to simple optimization techniques. Optimization techniques are selected based on analysis of performance and stability failure modes of compressive structural members. The objective of Shanley's approach was to establish a functional connection between the allowable stress value, on the one hand, and geometric parameters and the external load, on the other.
Because such a connection is rather difficult to establish due to the multi-parameter nature of the task, the number of variables needs to be reduced by expressing certain variables using an integrating factor. An effectively selected integrating factor can be a criterion of the minimal cross-section area (minimum weight) if actual stability failure modes of the compressive shape are considered. In this case, the maximum value of the integrating factor equals the minimum value of the cross-section area. If the thin wall shape buckles only in overall stability mode, then the integrating factor, named the “shape factor” by Shanley (KF=i2/F, where i and F are the radius of gyration and bar cross section area, respectively), can serve as the minimum weight criterion. If the compressive shape is also subject to local buckling, then the “shape factor” cannot serve as the criterion of minimum weight because its increase will result in reduction of the shape's bearing capacity (due to decrease in the local buckling critical stress).
It is a great challenge, from a design standpoint, to achieve optimum weight thin wall structures, especially, when one must also account for maximum expected load-bearing capacity along several cross-sections and different materials.
Thin wall structures are traditionally formed from thin wall profile members (TPMs) generally referred to as thin wall shapes. There are many applications where thin wall structures, due to low weight, are the only design choice for engineers and designers.
In some instances, in order to enhance the load-bearing capacity of thin wall shapes, the same TPMs may be “reinforced’ using reinforcing plates and/or shells (collectively referred to as “panels”). For purposes of discussion, we shall refer to reinforced TPMs as “TPM-panel combinations” or simply “TPM-panels”.
Structural design optimization has been developed, in general, for such simple structural members as thick wall beams, heavy cross-section bars, trusses, arches and frames. Thin wall plates, shells and shapes (TPMs) are significantly less researched.
In the same way as designing thick structures, thin wall structures must be designed to satisfy a variety of “constructive restrictions.” For example, the end design product must “fit” or “accommodate” the physical space for which it is designed. Other constructive restrictions may include, depending on the application, additional criteria such as weight, strength, stability, and flexibility constraints, as well as factors having to do with temperature (heat/cold resistance), conductivity, and other well-known material-selection criteria.
Modern design optimization relies heavily on computers which model and analyze a configuration to ensure that a particular design is suitable. Conventional tools, however, rely heavily on modeling techniques that draw mainly from thick wall structures, and which may be used for example to select an I-beam for a bridge or other extremely heavy load bearing project, where weight optimization, while important, it is not as critical as applications involving for example, aircrafts components.
Consequently, modern design of thin wall structures is focused more on single parameter-by-parameter optimization, with little emphasis on inter-dependencies of these parameters to other parameters. For example, critical stress, external compressed load, material properties, cross-section dimensions, and other criteria all impact, separately and interdependently, optimum design configuration and material selection.
Because inter-dependencies are not properly mapped out with the goal of weight optimizing a design for a given constructive restriction, the process is relatively unsophisticated.
It is desirable to be able to improve weight-optimization processes in design particularly in applications where TPMs may be employed.