topology optimization for structural collapse recovering

TOPOLOGY OPTIMIZATION F O R S T R U C T U R A L

COLLAPSE RECOVERING

by Davide Gamberini1, Ingrid Paoletti1, Roberto Naboni1

TECHNICAL CONFERENCE, Munich 26th june

1 DABC - Politecnico di Milano, via Ponzio 31, 20133, Milano, Italy.

Keywords: topology optimization, computational design, structural recover, retrofit structure

The paper address the problem of early adoption of software such as INSPIRE in the analysis of damages due to seismic assessment on existing masonry building.

A possible approach to simplify the form finding process of complicated structure such as retrofitting typology is presented, trying to understand limit of application of the soft-ware and the minimum required knowledge of the designer in the field of structural design.

ABSTRACT

STRUCTURE OF THE PAPER

USE INSPIRE

DESIGN METHODOLOGY

MATERIALS

MODEL SET-UP

CASE STUDY

COMPARISON OF THE RESULT

SEISMIC REINFORCING STRUCTURES

TOPOLOGICAL OPTIMIZATION

The purpose of topology optimization is to find the OPTIMAL LAY-OUT OF A STRUCTURE within a specified region when the only known design parameters are the applied loads, the possible support conditions, the volume of the structure to be constructed and possibly some

additional design restrictions such as the location and size of prescribed holes or solid areas (Martin, Bendsøe & Ole Sigmund, 2003).

Topological optimization logic ALREADY IMPLEMENTED in the field of retrofitting structures both concrete and carbon fibres (M. Bruggi, A. Talierci, 2013; M. Bruggi, G. Milani, A. Talierci, 2014)

MAX STIFFNESS 50% ORIGINAL VOLUME MAX STIFFNESS 30% ORIGINAL VOLUMESET UP DESIGN SPACE

USE OF INSPIRE

STRUCTURAL SOLVER with topological optimization logic implemented.

FRIENDLY USER INTERFACE it is easy to learn and practical to be used

PLATFORM for the designer who is not used to topological optimization problems

Our attempt is to understand if is possible to simplify the workflow and the study of these particular

structures:

DIFFICULT APPLICATION of topological optimization

EARLY FEEDBACK capable to guide the design process

INSPIRE

SIMPLIFIED STRATEGY proposed in the paper

REINFORCING SEISMIC STRUCTURE

FAST PROVVISION STRUCTURAL CONFIGURATIONS FOR CERTAIN LOAD CONDITIONS

UN-REINFORCED MASONRY STRUCTURES

RETROFITTING OF STRUCTURE

AESTHETIC MATTERS

HYPOTHESIS: to intervene on existing building and create an additional structure at the level of the facade, to reinforce an exhausted structure to recover from seismic activity damages or to prevent potential damages.

RESEARCH METHODOLOGY

1 - LOADS/ CONSTRAINS ANALYSIS

2 - INITIAL ANALYSIS

3 - REFINED ANALYSIS

4 - COMPARISON OF THE RESULTS

MATERIALS

This study involved thee different materials: steel, reinforced carbon fibres stripes and premixed ultra high performance concrete. The three options taken under consideration present different mechanical properties and fabrication process. Targeting the future

adoption of this technique, it is interesting to explore a range of structural solutions which can vary on different materials.

Table: Material specification implemented in the simulation processes.

PRE-MIXED ULTRA-HIGH PERFORMANCE CONCRETE

(UHPC)

CARBON FIBER STRIPES (CFRP) STEEL

UHPC

2500Density (Kg/m3)Compressive Strength

(MPa)

Young’s Modulus (MPa)

Poisson Coefficient

1600 7850

200 120 200

55 120 689

0,2 0,74 0,29

CFRP Steel

SET-UP OF THE MODEL

The correct configuration of the model passes through the understanding of the geometrical layout of the existing masonry structure itself.

LOADS: DESIGN SPACE: STRUCTURAL CONSTRAINTS:

POINT OF APPLICATION &DIRECTION AND TYPOLOGY

GEOMETRICAL DEFINITION

MATERIAL

LOAD BEARING ELEMENTS are identified on the existing building (foundations, kerbs, orthogonal walls)

DEGREE OF FREEDOM

ALLOWED DISPLACEMENTAMPLITUDE OF THE FORCES

Based on typological seismic damages schemes: collapse out of the plane

collapse on plane

Based on law verification standards on seismic structures

“Norme Tecniche per le Costruzioni D.M. del 14 gennaio 2008”

CALIBRATION OF THE MODEL

A series of SIMPLE ITERATIONS are produced with the aim to understand the behaviour of the software according with different typology of loads, constraints, maximum displacements allowed

and logic of computation.

MODEL SET-UP

SOLVER LOGICS: Max stiffness / Max refinement of the initial volume

CASE STUDY

MASONRY LOAD BEARING STRUCTURE

dimensions: L 10m/ H 10m / W 0,45m

MODEL GEOMETRICAL CHARACTERISTICS:

SCENARIO 1

Regional collapse out of the planeThe condition of the orthogonal structures DO permits support

SCENARIO 2

Regional collapse out of the planeThe condition of the orthogonal structures DO NOT permits support

SCENARIOS TAKEN IN CONSIDERATION:

SCENARIO 3

Retrofit to existing structureCollapse on the plane

The condition of the orthogonal structures DO NOT permits support

All the iterations taken into account for the case studies are obtained following the maximum stiffness logic (with targeted mass 30% of the original design space).

SCENARIO 1

DESCRIPTION OF THE LOAD CASE:

36 KN applied in the normal direction on the surfacemoment with a value of the 25 KN.m.

Constraint Points on horizontal Curbs. Allowed displacement 0,02 m

Number of elements computed: 26949objective function change of volume: -83,3%

maximum displacement: 0.214 mMax Stress: 0,112E+08

CONCRETE STRUCTURE



STEEL STRUCTURE



CARBON FIBRES STRIPES

COLLAPSE OUT OF PLANE WITH USE OF THE ORTHOGONAL WALLS

RESULTS OF COMPUTATION:

SCENARIO 2

CONCRETE STRUCTURE CARBON FIBRES STRUCTURE STEEL STRUCTURE








COLLAPSE OUT OF PLANE WITHOUT THE USE OF THE ORTHOGONAL WALLS


36 KN applied in the normal direction on the surfacemoment with a value of the 25 KN.m.

Constraint Points selected on the foundation. Allowed displacement 0,02 m

SCENARIO 3

Number of elements computed: 26995Objective function change of volume: -81,8%

Max displacement: 0.0016 mMax Stress: 0,140E+08





COLLAPSE IN PLANE / RETROFITTED STRUCTURE

CONCRETE STRUCTURE CARBON FIBRES STRUCTURE STEEL STRUCTURE



55 KN applied in the longitudinal direction on the surfacein correspondency of the openings

Constraint Points selected on the foundation, first floor and roof Curbs. Allowed displacement 0,02 m

COMPARISON OF RESULTS

Results of the computation of the three case study are compared based on: percentage of volume subtracted from the facade, maximum stress, maximum displacement, percentage of covering of the facade, possibility to be fabricate.

% SUBTRACTED VOLUME MAX DISPLACEMENT % COVERING OF FACADE FABRICATION PROCESSMAX STRESSES

1 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 4

lower than 69,9% Higher stress Max displacement reached More than 30,1% shape and fabrication process is not compatible

from 70,0% to 79,9% High stress case Higher than 50% of the range Between 30,0% and 20,1% difficult shape and fabrication process match

from 80,0% to 89,9% Low stress case Lower than 49,9% of the range Between 20,0% and 10,1% easy shape and fabrication process match

over 90,0% Lower stress No displacement Less than 10,0% shape and fabrication process are matching

FINAL COMMENTS ON THE STRUCTURES

Steel Structure

Steel Structure

Steel Structure

CFRP Structure

CFRP Structure

CFRP Structure

UHCP Structure

UHCP Structure

UHCP Structure

SCENARIO 3CFRP is the best choice for reinforcing existing masonry structure.

BENEFITS: lower maximum stress, lower facade’s surface covering and higher feasibility in the fabrication process.

SCENARIO 1UHCP is the best material option among the others.

BENEFITS: lower maximum stress, lower facade’s surface covering.SCENARIO 2

STEEL is the best material choice for the structure.BENEFITS: lower maximum stress, higher % original volume discarded, lower facade’s surface covering.

INSPIRE FEEDBACK

POSSIBLE IMPROVEMENTS OF THE SOFTWARE:

NEEDS FOR POWERFUL HARDWARE SETUP (Especially in the evaluation of thinner elements)

IMPLEMENTATION OF INTER-OPERABILITY (Characteristic that is very important and ensures faster and better results)

VISUAL ESTIMATIVE TOOLS (To provide immediate feedback on results with coloured mesh)

USER FRIENDLY INTERFACE ( fast to learn but in advanced stage can be an obstacle)

USEFUL TOOL FOR NOT EXPERIENCED DESIGNER ( the knowledge of the user on structural subjects must be broad and deep )

FAST DESIGN FEEDBACK( it is possible to compare different solutions and

decide the direction in the early design phase)

FUTURE PERSPECTIVES

PROPOSED FUTURE DEVELOPMENT OF THIS PAPER:

TO FINALIZE THE DESIGN OF THE REINFORCING STRUCTURES(with an advanced tool such as Optistruct)

TO ENSURE THE FEASIBILITY THROUGH FABRICATION PROCESS

APPLICATION OF A GENERATIVE ALGORITHM (Providing to the user the possibility to adopt

the outcome of the comparative matrix automatically)

SET UP of the simulation model

Usage of INSPIRE for topological optimization of reinforcing seismic structure

Case studies ANALYSIS

METHODOLOGY for this research

Usage of different MATERIALS

SUMMARISING

THANK YOU!

CONTACTS:

DAVIDE GAMBERINI [email protected]

topology optimization for structural collapse recovering

Engineering