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Design analysis of spherical pressure vessel


The aim of this test case is to validate the following functions:

  • Transient thermostructural analysis

The simulation results of SimScale were compared to the analytical results presented in [Amir14].

Import validation project into workspace


Geometry of the 1/8th sphere
x [m]00.1900.200
y [m]0.1900.2000
z [m]00000.190.2

Analysis type and Domain

Tool Type : Calculix, Code_Aster

Analysis Type : Transient Thermostructural

Mesh and Element types :

CaseMesh typeNumber of nodesElement typeValue of KappaTool type
(A)linear tetrahedrals1643443D isoparametric20Calculix
(B)linear tetrahedrals1643443D isoparametric20Code_Aster
(C)linear tetrahedrals1643443D isoparametric22Calculix
(D)linear tetrahedrals1643443D isoparametric22Code_Aster
Mesh used for analysis on SimScale platform

Simulation Setup


  • isotropic: E = 190 GPa, ν = 0.305,ρ = 7750 kg/m³, Kappa = 20 W/(m.K) & 22 W/(m.K), Expansion coefficient = 9.7e-6 1/K, Reference temperature = 300 K, Specific heat = 486 J/K

Initial conditions:

  • Temperature = 300 K


  • Face AECF zero x-displacement
  • Face BEDF zero y-displacement
  • Face ABCD zero z-displacement


  • Face ABE linear increasing pressure from 0 MPa to 1 MPa according to formula P = (0.2e6).t, where ‘t’ is time from 0 to 5 sec


  • Face ABE linear increasing temperature from 300 K to 500 K according to formula T = 40t + 300, where ‘t’ is time from 0 to 5 sec

Heat flux:

  • Face CDF convective heat flux of h = 90 W/(m².K) with reference temperature of 300 K


Comparison of the results with [Amir14]

Since no value of conductivity (kappa) was provided, the values of 20 W/(m.K) and 22 W/(m.K) were used. Comparison of vonMises stress (MPa) and temperature (K) computed over the edge EF with [Amir14] at final timestep are given below.


[Amir14](123) Amir Afkar,Majid Nouri Camari, Amin Paykani, Design and analysis of a spherical pressure vessel using finite element method,England, UK, World Journal of Modelling and Simulation, Vol. 10 (2014) No. 2, pp. 126-135

Last updated: January 29th, 2019

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