ANSYSBasic Concepts for ANSYS Structural Analysis

2/48

Contents1 Disciplines and Element Types2 Analysis Types3 Linear Analysis and Nonlinear

Analysis4. Material Models5. Failure Criteria of Materials

3/48

• Structural Analysis• Thermal Analysis• Fluid Dynamic Analysis• Electric Field Analysis• Magnetic Field Analysis• Coupled-field Analysis

Disciplines and Element Types

4/48

• Example 1: Thermal Stress Analysis• Example 2: Structure-Fluid Interactions• Example 3: Thermal Actuator

Examples

5/48

Element Types

• ANSYS elements are classified according to– Discipline– Dimensionality– Geometry– Order

• Example– SOLID45: 3D hexahedral linear structural

element– PLANE67: 2D quadralateral linear coupled

thermal-electric element

6/48

Analysis Types

• Static Analysis• Dynamic Analysis

– Transient Analysis– Modal Analysis– Harmonic Response

Analysis– etc.

• Buckling Analysis

• Structural Analysis– Static, Transient, Modal,

Harmonic, Buckling, etc.• Thermal Analysis

– Steady-state, Transient• Electric Field Analysis

– Static, Transient, Modal, Harmonic

• etc.

7/48

Transient Analysis

• Inertia forces• Damping forces• Elastic forces• External forces

FKDDCDM

8/48

Static Analysis

• When dynamic effects can be neglected, a problem can be solved statically.

• Dynamic effects can be neglected only when the deformation velocity and acceleration are small.

• Two cases:– Steady-state solution– approximation solution for a real-world

problem.

FKD

9/48

Modal Analysis

• Modal analysis is to analysis a structure under free vibration.

• The solutions typically include– Vibration frequencies (or periods)– Vibration modes

0KDDCDM

10/48

Harmonic Response Analysis

• Harmonic response analysis is to analysis a structure under periodic excitation of external forces.

• The solutions typically include maximum responses under various frequencies of external forces

11/48

Linear Analysis and Nonlinear Analysis

12/48

Linear Analysis

• Small deformation• Hooke’s law appies• No status or

topological changes, eg., contacts

Loads

Responses

13/48

Nonlinear Analysis

• Geometric nonlinearity• Material nonlinearity• Status nonlineaity

14/48

Material Models

• Material models are mathematically represented by a set of equations called constitutive equations.

• The constitutive equations describe the relations between stresses and strains (or strain rates).

• The parameters in the constitutive equations are called material parameters.

• ANSYS provides many material models to be chosen from.

15/48

Elastic vs. Plastic

Elastic materials(a) Nonlinear elastic(b) Hysteresis elastic(c) Linear Elastic

Stress

Strain

(a)

Stress

Strain

(b)

(c)

Stres

s

Strain

16/48

Elastic vs. Plastic

Plastic materials

Strain

Stress

17/48

Viscous vs. Nonviscous

Nonvisousmaterials

Time

Stress

TimeS

train

18/48

Viscous vs. Nonviscous

Visousmaterials

Stress

Strain

Time

Time

19/48

Viscous vs. Nonviscous

Creeping

Time

Stress

Time

Strain

Time

Strain

Time

Stress

Stress Relaxation

20/48

Homogeneous vs. Heterogeneous

• A material body is said to be homogeneous if it has uniform material properties everywhere in the body.

• Otherwise it is said to be heterogeneous.• Note that, homogeneousness does not

necessarily imply isotropy.

21/48

Isotropic, Anisotropic, and Othothropic Materials

• A material is said to be isotropic if it has the same material properties along any directions in the body.

• Otherwise it is said to be anisotropic.• An anisotropic material is said to be

orthotropic, if the planes of material symmetry are mutually orthogonal.

22/48

Isotropic, Anisotropic, and Othothropic Materials

G

G

G

EEE

EEE

EEE

zxzx

yzyz

xyxy

zyxz

zyxy

zyxx

Dσε

zx

zxzx

yz

yzyz

xy

xyxy

y

yzy

x

xzx

z

zz

x

xyx

z

zyz

y

yy

z

zxz

y

yxy

x

xx

G

G

G

EEE

EEE

EEE

Hooke’s Law for Isotropic Material

Hooke’s Law for Anisotropic

Material

Hooke’s Law for Orthotropic

Material

z

zx

x

xz

z

zy

y

yz

y

yx

x

xy

EE

EE

EE

23/48

Failure Criteria of Materis

24/48

Ductile vs. Brittle

Ductile Material

Strain

Stress

Strain

Stress

Brittle Material

25/48

Failure Criteria for Brittle Materials

Maximum Principal Stress Failure Criteria:• Fracture will occur when tensile stress is

greater than ultimate tensile strength, i.e.,

u 1

26/48

Failure Criteria for Ductile Materials

Tresca Failure Criteria:• Yielding will occur when shear stress is

greater than shear yield strength, i.e.,

2231 y

y 31

or

27/48

Failure Criteria for Ductile Materials

von Mises Failure Criteria:• Yielding will occur when the von Mises

stress is greater than yield strength, i.e.,

ye 213

232

2212

1