Static Stress Redesign of Plates by Large Admissible Perturbations

2005 ◽  
Author(s):  
Bhineka M. Kristanto ◽  
Michael M. Bernitsas
Keyword(s):  
Plate Thickness ◽  
Forced Response ◽  
Static Stress ◽  
Perturbation Equation ◽  
Shell Elements ◽  
Modal Properties ◽  
General Perturbation ◽  
Structure Changes ◽  
Admissible Perturbation ◽  
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.

Static Stress Redesign of Plates by Large Admissible Perturbations

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Bhineka M. Kristanto ◽  
Michael M. Bernitsas
Keyword(s):  
Finite Element Analysis ◽  
Plate Thickness ◽  
Forced Response ◽  
Static Stress ◽  
Perturbation Equation ◽  
Element Analysis ◽  
Shell Elements ◽  
Structure Changes ◽  
The Finite Element Analysis ◽  
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 Structures by Large Admissible Perturbations

2003 ◽  
Vol 127 (2) ◽  
pp. 122-129 ◽  
Author(s):  
Michael M. Bernitsas ◽  
Bhineka M. Kristanto
Keyword(s):  
Cross Section ◽  
Forced Response ◽  
Static Stress ◽  
Neutral Axis ◽  
Perturbation Equation ◽  
Cross Sectional ◽  
Structure Changes ◽  
Large Admissible Perturbations ◽  
The Cross ◽  
Outer Fiber

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.

Static Stress Redesign of Structures by Large Admissible Perturbations

2003 ◽  
Author(s):  
Michael M. Bernitsas ◽  
Bhineka M. Kristanto
Keyword(s):  
Cross Section ◽  
Forced Response ◽  
Static Stress ◽  
Neutral Axis ◽  
Perturbation Equation ◽  
Cross Sectional ◽  
Structure Changes ◽  
Large Admissible Perturbations ◽  
The Cross ◽  
Outer Fiber

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 Submerged Structures by Large Admissible Perturbations

2001 ◽  
Vol 123 (3) ◽  
pp. 103-111 ◽  
Author(s):  
Vincent Y. Blouin ◽  
Michael M. Bernitsas
Keyword(s):  
Finite Element ◽  
Optimization Problem ◽  
Mass Matrix ◽  
Added Mass ◽  
Forced Response ◽  
Initial Structure ◽  
General Perturbation ◽  
Large Admissible Perturbations ◽  
Fluid Added Mass ◽  
Perturbation Equations

The method of large admissible perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures without trial and error or repetitive finite element analyses. When forced vibration constraints are incorporated into the redesign problem, damping and added mass due to the presence of fluid must be included into the model. The corresponding terms introduce theoretical and numerical difficulties, which are treated in this paper. The LEAP method has been implemented into a Fortran computer code RESTRUCT, developed at the University of Michigan. The redesign process is mathematically formulated as an optimization problem with nonlinear constraints, called general perturbation equations. First, a finite element analysis of the initial structure is executed. Then, the results are postprocessed by code RESTRUCT using an incremental scheme to find the optimum solution for the problem defined by the designer. Accurate determination of nonstructural terms, such as fluid added mass, is generally detrimental as far as forced response analysis is concerned. In redesign problems, however, simple but realistic models can be used. A simple transformation of the structural mass matrix is used to compute the added mass matrix and its dependency on the redesign variables. The presence of non-structural terms in the general perturbation equations requires the development of a new LEAP algorithm for solution of the optimization problem. A simple cantilever beam with 100 degrees of freedom is used to validate the fluid added mass model. The developed method and algorithm are then applied to a partially submerged 4,248 degree of freedom complex structure modeled with beam elements.

Treatment of Damping in Structural Redesign by Large Admissible Perturbations

1999 ◽  
Author(s):  
Vincent Blouin
Keyword(s):  
Structural Characteristics ◽  
Forced Response ◽  
Mode Shapes ◽  
Perturbation Equation ◽  
Structural Damping ◽  
Design Problems ◽  
Damping Matrix ◽  
Structural Redesign ◽  
Large Admissible Perturbations ◽  
External Forces

Abstract A method to solve redesign (inverse design) problems of complex structures with forced response amplitude constraints is developed. It is assumed that a structure is excited by harmonic external forces at a given frequency. The problem is to find optimum values of structural characteristics in order to achieve a desired level of forced response at one or several locations on the structure. The method of LargE Admissible Perturbations (LEAP) is used. Damping is shown to have an important impact on the redesign solution and must be considered in the redesign process. Two different treatments of the damping, leading to two different algorithms, are studied. In the case of structural damping, the commonly used Rayleigh formulation allows the damping matrix to be diagonalized by use of the real mode shapes of the undamped structure. This leads to the derivation of an exact perturbation equation with no loss of accuracy. When damping cannot be approximated by the Rayleigh model, the damping matrix must be treated externally and the perturbation equation is solved by means of an iterative process introduced into the redesign algorithm. The two algorithms are compared in terms of accuracy and limitations.

Structural Redesign by Large Admissible Perturbations With Static Mode Compensation

1999 ◽  
Vol 121 (1) ◽  
pp. 39-46 ◽  
Author(s):  
M. M. Bernitsas ◽  
D. Suryatama
Keyword(s):  
Structural Changes ◽  
Minimum Weight ◽  
Original Structure ◽  
Perturbation Equation ◽  
Static Properties ◽  
Static Mode ◽  
General Perturbation ◽  
Static Performance ◽  
Large Admissible Perturbations ◽  
New Formulation

The method of LargE Admissible Perturbations (LEAP) solves redesign problems of complex structures without trial and error or repetitive finite element analyses. Code RESTRUCT (Redesign of STRUCTures) produces an optimal redesign of minimum structural change or minimum weight with modal dynamics and/or static displacement specifications. LEAP allows for large structural changes. First, the general perturbation equations are derived relating the original structure S1 (known) to the objective structure S2 (unknown) which is to satisfy the designer’s specifications. Next, the redesign problem is solved using an incremental prediction-correction scheme. In the past, LEAP produced accurate results even for 100–300 percent changes in redesign for modal objectives without any intermediate FEAs. Accuracy in static redesign, however, was limited to about 50 percent changes in static objectives. In this work, a new static general perturbation equation and the corresponding LEAP algorithm are developed to achieve accuracy for 100–300 percent changes in static performance as well. The new formulation includes the static deflection shape as the zeroth mode in the expansion of static properties in terms of dynamic modes. Systematic numerical applications show that high accuracy is achieved by fewer extracted modes.

Integrated Redesign of Large-Scale Structures by Large Admissible Perturbations

2003 ◽  
Vol 125 (4) ◽  
pp. 234-241 ◽  
Author(s):  
Vincent Y. Blouin ◽  
Michael M. Bernitsas ◽  
Denby Morrison
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Direct Method ◽  
Computational Effort ◽  
Forced Response ◽  
Response Amplitude ◽  
Computational Time ◽  
Performance Constraints ◽  
Large Admissible Perturbations ◽  
Design Selection

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.

Cognate Space Identification for Forced Response Structural Redesign

2003 ◽  
Vol 127 (3) ◽  
pp. 227-233
Author(s):  
Vincent Y. Blouin ◽  
Michael M. Bernitsas
Keyword(s):  
Direct Method ◽  
A Priori ◽  
Normal Modes ◽  
Forced Response ◽  
Response Amplitude ◽  
Computational Time ◽  
Practical Guidelines ◽  
Structural Redesign ◽  
Large Admissible Perturbations ◽  
Perturbation Equations

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.

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