Structural Responses – One of the Key Ingredients for Defining Structural Optimization Problems

Juan Pablo Leiva
Juan Pablo Leiva New Altair Community Member
edited November 2023 in Altair HyperWorks

Product = GENESIS

 

 

Introduction

 

Structural optimization is used to efficiently improve structures. Its usage requires the selection of two sets of quantities:  Design variables and Responses. Design variables correspond to parameters that describe or define the structure, while responses correspond to quantities used to define the objective and the constraints of the problem. Responses can come from finite element analysis, geometry parameters, or a combination of the two. 

 

In this blog we will describe some of the key responses available in the GENESIS structural analysis and optimization software.

 

Responses Available in GENESIS

 

Responses are quantities that are calculated by the program and are typically functions of the design variables. They can be used as the objective function or as constraints of the optimization problem. Understanding what responses are available allows the user to understand the power and the capabilities of the software. A summary of the responses available in GENESIS is presented next.

 

Finite Element Responses

 

Almost every finite element response calculated for analysis can be used in optimization. These responses are:

 

  • Static responses:  Displacements, stresses, strain forces, reaction forces and strain energy
  • Heat transfer responses: Temperatures and heat compliance
  • Stability analysis responses: Buckling load factors
  • Vibration analysis responses: Natural frequencies and mode shape components
  • Dynamic and Random responses:  Displacements, velocities, accelerations; stresses, strains, forces and ERP (Equivalent Radiated Power)
  • Acoustic responses: Acoustic pressures
  • Fatigue responses: Stresses and strain responses

 

Figure 1 – Stress Distribution

 

 

 

Fig. 1 shows the stress distribution on a structural component. Any or all stress shown there can be used as a response to define constraints on an optimization problem.

 

Geometry Responses

 

Geometry Responses are responses that are functions of grid locations. Examples are: volumes, areas, lengths, angles, distances, moment of inertias and center of gravity.

 

Figure 2 – Angle response

 

 

 

Fig. 2 shows an angle defined using 3 grids of a finite element mesh. This angle can be used as a response to define a constraint on a shape, topography, and/or freeform optimization problem.

 

Equation Responses

 

The user can specify nonlinear equations combining finite element responses, design variables, grid locations, and geometric responses to create their own responses.

 

Figure 3 – User Equation

 

 

 

Fig. 3 shows a user equation including a Force F response and an area A of a bar. This equation response can be used as a response to prevent local buckling of a bar element on an optimization problem.

 

Shifted Responses

 

The user can specify a built-in equation that is a function of frequencies to scale, invert, offset, etc. and responses that themselves are a function of frequencies.

 

Figure 4 – Shifted Response

 

 

 

Fig. 4 shows one of several optional shifted response equations available in GENESIS. The equation shown allows the user to scale by Coeff and to convert to Log Scale H(f)/Refval.  In the above equation H(f) could be displacements, velocities, acceleration or other frequency dependent FEA responses and Refval is a real value supplied by the user.  T(f) is a table value that is a function of frequencies.  

 

Subroutine Responses

 

User-written subroutines can be linked with GENESIS to mix finite element responses, design variables, grid locations and geometric responses to create special responses.

 

External Responses

 

An external program can be called within GENESIS to generate responses from the external analysis programs for multidisciplinary optimization.   Examples are:  Non-Linear Displacement from LS-Dyna or Non-Linear stresses and strains from ANSYS.

 

Examples using Responses Available in GENESIS

 

Depending of what kind of structure is desired, the user can pick and choose one or more of the available responses as the objective and the additional responses as constraints.  Here are some examples:

 

 

 

Lightest Structure Possible

 

The following formulation can be used:

 

Figure 5 – Optimization Problem Statement to Obtain a Light Structure

 

 

 

Stiffest Structure Possible

 

The following formulation can be used:

 

Figure 6 – Optimization Problem Statement to Obtain a Stiff Structure

 

 

 

Most Conductive Structure Possible

 

The following formulation can be used:

 

Figure 7 – Optimization Problem Statement to Obtain a Conductive Structure

 

 

 

 

 

Discussion and Summary

 

Responses in the GENESIS software are used to define the objectives and constraints in a structural optimization problem. The GENESIS user can choose from a large variety of responses and he/she can mix them in a single problem. The user can simultaneously use responses from static, dynamic, heat transfer, and/or other analysis types.  These responses can be used on sizing, shape, topology, topometry, topography, and/or freeform optimization problems.

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