Users:Structural Optimization/Response Functions/Mass

Contents 1 General Description 1.1 Short Info 2 Input Parameters 2.1 Example of a Complete Input Block 3 Examples 3.1 Catenoid 3.2 Scherkian Minimal Surface 4 References

General Description

Short Info

This response function controls the mass of a finite element system. The value of this response function represents the overall system mass M of all elements computed by summation of all element masses m_i.

Input Parameters

Block headline
Parameter	Values, Default(*)	Description
OPT-RESPONSE_FCT	int : MASS	Function ID and type mechanical problem.
Common compulsory parameters
ETA	real	Finite difference disturbance for sensitivity analysis
GRAD	DIRECT, ADJOINT	Method of gradient computation
SA	GLOBAL_FD, SEMI_ANALYTIC, EXACT_SEMI_ANALYTIC, ANALYTIC	Method of derivative computations inside sensitivity analysis
FDA	FOREWARD, CENTRAL, BACKWARD	Method of finite difference approximation (if neccessary for the chosen sensitivity analysis method)
DESVAR	OPT-VAR vector of integers	Design variables that are considered in the sensitivity analysis of this response function
Common optional parameters
WEIGHT	real, 1.0*	The weighting factor for this response function in multi-objective optimization
ANALYSIS	PC-ANALYSIS int	ID of the underlying analysis
Specific parameters
DOMAIN	EL-DOMAIN int	ID of system domain
Common Compulsory Parameters for Constraints
Parameter	Values, Default(*)	Description
REL_LIMIT	real	Relative limit for constraint, depending on the actual value.
ABS_LIMIT	real	Absolute limit for constraint. Only one limit can be defined for a constraint.
CONSTRAINT_TYPE	INEQUALITY_LT, INEQUALITY_GT, EQUALITY	Type of constraint
Common Optional Parameters for Constraints
REL_TOLERANCE	real, 0*	Upper relative limit until which an inactive constraint is concidered as an active one
LAMBDA_ABS_MAX	real, 1/cepsilon*	Upper limit for lagrangian multiplier

Example of a Complete Input Block

OPT-RESPONSE_FCT 1 : MASS

  ! -- basic stuff
  WEIGHT=1.0  ETA=1e-06
  GRAD=ADJOINT SA=SEMI_ANALYTIC FDA=FOREWARD
  DESVAR=OPT-VAR 1,2,3,4,5,6

  ! -- response function dependant parameters
  DOMAIN = EL-DOMAIN 1

  ! -- constraint parameters
  ABS_LIMIT = 1-e3
  REL_TOLERANCE = 0.1
  CONSTRAINT_TYPE = INEQUALITY_LT
  LAMBDA_ABS_MAX = 20

Examples

Catenoid

This example considers the mass minimization of a simple catenoid structure. A catenoid can be designed by rotation of the catenary curve^[1]. Due to the constant density and thickness it is equivalent to the pure mathematical minimal surface problem. The catenoid as a minimal surface was found by Leonard Euler ^[2] in 1744. Another principle to compute minimal surfaces is the Formfinding with isotropic pre-stress fields.

• 

  Initial Catenoid Geometry

• 

  Optimal Catenoid Geometry (Minimal Surface equal to Minimal Mass)

Scherkian Minimal Surface

A second example shows another famous minimal surface, namely the so called Scherkian minimal surface^[3]. It was found by Heinrich Ferdinand Scherk^[4] in 1835.

• 

  Initial Geometry

• 

  Optimal Scherkian Surface (Minimal Surface equal to Minimal Mass)

References

1. ↑ http://en.wikipedia.org/wiki/Catenary
2. ↑ http://de.wikipedia.org/wiki/Leonhard_Euler
3. ↑ http://de.wikipedia.org/wiki/Minimalfl%C3%A4che#Die_Minimalfl.C3.A4che_von_H._F._Scherk
4. ↑ http://de.wikipedia.org/wiki/Heinrich_Ferdinand_Scherk

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