Structural optimization of stress-bearing structures of nearly incompressible problems under design-dependent pressure loads

doi:10.1007/s10483-026-3368-6

Abstract

Abstract:

An efficient and innovative method is presented for the stress-related structural topology optimization (TO) in coupled mechanical-pressure systems by leveraging flexible polygonal meshes. With a polytopal composite finite element approach, the volumetric locking in nearly incompressible materials is reduced. A fluid-flow-based model is built, in which a design-dependent pressure variable is introduced to capture the loading conditions within the system. The P-norm approach consolidates the stress metrics into a global measure, while the clustered regional scaling and adaptive techniques enhance the solutions for stress-limited cases. The primary contributions of this work include a novel framework for addressing the stress challenges in coupled mechanical-pressure systems via flow-based modeling, the adaptability to both compressible and nearly incompressible materials, and the compatibility with diverse mesh types, including triangular, quadrilateral, and polygonal elements. The numerical examples demonstrate, for the first time, optimized topologies for nearly incompressible materials under stress constraints in coupled mechanical-pressure environments, emphasizing the unique strength of this approach.

Key words: topology optimization (TO), stress-related problem, design-dependent load, near incompressibility, mechanical-pressure system, polytopal composite finite element

2010 MSC Number:

O302

T. T. BANH, N. T. Y. NGUYEN, H. P. BAN, D. LEE. Structural optimization of stress-bearing structures of nearly incompressible problems under design-dependent pressure loads. Applied Mathematics and Mechanics (English Edition), 2026, 47(4): 905-926.

TrendMD

Figures/Tables 14

Fig. 1

Table 1

Comparison of different objectives and constraints of the closed planar container"

Case	Optimized design	Stress plot
Case 1: Minimum compliance design under volume constraint (20%V₀) when $σ max = 842.07 MPa$ and $V = 20.00 %$
Case 2: Minimum volume design under stress constraint $(σ adm = 250 MPa)$ when $σ max = 250.00 MPa$ and $V = 20.13 %$
Case 3: Minimum stress design under volume constraint (20%V₀) when $σ max = 258.48 MPa$ and $V = 20.00 %$

Table 1

Fig. 2

Fig. 3

Fig. 4

Table 2

Comparison of stress designs between the discrete methods under different conditions"

	Plane stress		Plane strain
	PCEs	PEs	PCEs	PEs
Compressibility ( $ν 0 = 0.3$ )
Near incompressibility ( $ν 0 = 0.499 99$ )

Table 2

Fig. 5

Fig. 6

Table 3

Comparison of the optimal arches under different pressure intensities"

Case	Optimized design	Stress plot
Case 1: $p 0 = 5 MPa,$ $V = 10.90 %,$ and $σ max = 75.81 MPa$
Case 2: $p 0 = 7 MPa,$ $V = 15.00 %,$ and $σ max = 75.79 MPa$
Case 3: $p 0 = 9 MPa,$ $V = 20.19 %,$ and $σ max = 75.80 MPa$

Table 3

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

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