Static Stress Redesign of Plates by Large Admissible Perturbations

The purpose of this paper is to develop further the large admissible perturbation (LEAP) methodology to solve the static stress redesign problem for shell elements. The static stress general perturbation equation, which expresses the unknown stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends on the redesign variables for each element or group of elements, namely, the plate thickness. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT, which postprocesses the finite element analysis FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive FEAs. Several numerical applications on a simple plate and an offshore tower are used to verify the effectiveness of the LEAP algorithm for stress redesign.

Static Stress Redesign of Plates by Large Admissible Perturbations

The LargE Admissible Perturbation (LEAP) methodology is developed further to solve static stress redesign problems for shell elements. The static stress general perturbation equation, which expresses the unknown stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends on the redesign variables for each element or group of elements; namely the plate thickness. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT which post-processes the FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive FEA’s. Several numerical applications on a simple plate and an offshore tower are used to verify the LEAP algorithm for stress redesign.

Integrated Redesign of Large-Scale Structures by Large Admissible Perturbations

In structural redesign (inverse design), selection of the number and type of performance constraints is a major challenge. This issue is directly related to the computational effort and, most importantly, to the success of the optimization solver in finding a solution. These issues are the focus of this paper, which provides and discusses techniques that can help designers formulate a well-posed integrated complex redesign problem. LargE Admissible Perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, free vibration, static deformation, and forced response amplitude constraints. The existing algorithm, referred to as the Incremental Method is improved in this paper for problems with static and forced response amplitude constraints. This new algorithm, referred to as the Direct Method, offers comparable level of accuracy for less computational time and provides robustness in solving large-scale redesign problems in the presence of damping, nonstructural mass, and fluid-structure interaction effects. Common redesign problems include several natural frequency constraints and forced response amplitude constraints at various frequencies of excitation. Several locations on the structure and degrees of freedom can be constrained simultaneously. The designer must exercise judgment and physical intuition to limit the number of constraints and consequently the computational time. Strategies and guidelines are discussed. Such techniques are presented and applied to a 2,694 degree of freedom offshore tower.

Static Stress Redesign of Structures by Large Admissible Perturbations

The LargeE Admissible Perturbation (LEAP) methodology is developed further to solve static stress redesign problems. The static stress general perturbation equation, which expresses the unknown nodal stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends on the redesign variables for each element or group of elements; namely, the cross-sectional area and moment of inertia, and the distance between the neutral axis and the outer fiber of the cross section. This equation preserves the shape of the cross section in the redesign process. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT which post-processes the FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive finite element (FE) analyses. Several numerical applications on a simple cantilever beam and an offshore tower are used to verify the LEAP algorithm for stress redesign.

Selection of Variables for Structural Redesign by Large Admissible Perturbations

Redesign or inverse design is the process of generating a new optimal design which satisfies performance specifications starting from a baseline design with undesirable performance. The LargE Admissible Perturbation (LEAP) methodology makes it possible to redesign a structure for large changes in performance objectives and redesign variables without trial and error or repetitive finite element analyses. The next level of challenge in redesign automation is to identify a priori the structural elements and their properties that have the biggest impact and use only those in redesign. Based on LEAP, guidelines are developed in this paper for identifying effective selection of redesign variables for improved accuracy and reduced CPU time. These guidelines enable the designer to define the elements to be redesigned, to partition those elements among redesign groups, and to specify redesign variables in each group. In the numerical applications, an offshore tower is used to verify the developed guidelines. Three models of this tower with 160, 320, and 480 elements are used.

Cognate Space Identification for Forced Response Structural Redesign

Large admissible perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, forced response amplitude constraints. In previous work, two LEAP algorithms, namely the incremental method (IM) and the direct method (DM), were developed. A powerful feature of LEAP is the general perturbation equations derived in terms of normal modes, the selection of which is a determinant factor for a successful redesign. The normal modes of a structure may be categorized as stretching, bending, torsional, and mixed modes and grouped into cognate spaces. In the context of redesign by LEAP, the physical interpretation of a mode-to-response cognate space lies in the fact that a mode from one space barely affects change in a mode from another space. Perturbation equations require computation of many perturbation terms corresponding to individual modes. Identifying modes with negligible contribution to the change in forced response amplitude eliminates a priori computation of numerous perturbation terms. Two methods of determining mode-to-response cognate spaces, one for IM and one for DM, are presented and compared. Trade-off between computational time and accuracy is assessed in order to provide practical guidelines to the designer. The developed LEAP redesign algorithms are applied to the redesign of a simple cantilever beam and a complex offshore tower.

Selection of Variables for Structural Redesign by Large Admissible Perturbations

Redesign or inverse design is the process of generating a new optimal design which satisfies performance specifications starting from a baseline design with undesirable performance. The LargE Admissible Perturbation (LEAP) methodology makes it possible to redesign a structure for large changes in performance objectives and redesign variables without trial and error or repetitive finite element analyses. The next level of challenge in redesign automation is to identify a priori the structural elements and their properties that have the biggest impact and use only those in redesign. Based on LEAP, guidelines are developed in this paper for identifying effective selection of redesign variables for improved accuracy and reduced CPU time. These guidelines enable the designer to define the elements to be redesigned, to partition those elements among redesign groups, and to specify redesign variables in each group. In the numerical applications, an offshore tower is used to verify the developed guidelines. Three models of this tower with 160, 320, and 480 elements are used.

Static Stress Redesign of Structures by Large Admissible Perturbations

The LargE Admissible Perturbation (LEAP) methodology is developed further to solve static stress redesign problems. The static stress general perturbation equation, which expresses the unknown nodal stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends the on the redesign variables for each element or group of elements; namely, the cross-sectional area and moment of inertia, and the distance between the neutral axis and the outer fiber of the cross section. This equation preserves the shape of the cross-section in the redesign process. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT which post-processes the FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive FE analyses. Several numerical applications on a simple cantilever beam and an offshore tower are used to verify the LEAP algorithm for stress redesign.

Redesign of Cylindrical Shells by Large Admissible Perturbations

Structural redesign is the process of finding a new design that satisfies a set of performance requirements starting from a poorly performing design. Structural redesign is formulated as a two-state problem where the baseline design exhibits undesirable response characteristics and the objective design satisfies the design requirements. A LargE Admissible Perturbations (LEAP) methodology is developed to formulate and solve the problem of structural redesign of cylindrical shells for modal dynamics. First, the nonlinear perturbation equations of cylindrical shells for modal dynamics are derived relating the baseline to the unknown objective design. The redesign problem is formulated as an optimization problem. Next, an algorithm is developed to solve the nonlinear problem and to identify a locally optimal design that satisfies the given modal dynamics specifications. The developed LEAP algorithm calculates incrementally without trial and error or the repetitive finite-element analyses the structural design variables of the objective design. Numerical applications of cylindrical shell redesign for modal requirements are used to verify the methodology and test the algorithm. The developed methodology identifies incompatible frequency requirements where solutions cannot be achieved. Further, systematic redesign applications show that even for strip uniform shells, modes are linked, making satisfaction of multiple frequency objectives impossible.