Application of Numerical Simulation Technology in Engineering Management and its Impact on Project Costs

The research field of numerical simulation technology integrates a variety of disciplines, including computer science, mathematics, materials science, mechanics, engineering technology and other disciplines. The basic process of numerical simulation includes: firstly, set the initial conditions based on the existing experimental environment data, and establish the simulation model, then simulate the experiment in the simulation program, and calculate the simulation results, and finally explore the laws through the calculation results [1-4]. Compared with the traditional experimental operation and theoretical analysis methods, numerical simulation technology has the advantages of short experimental cycle, can be multi-factor coupling, and the output results are intuitive [5-7]. Especially in the field of material corrosion and protection in engineering management, the use of numerical simulation technology combined with experimental research and theoretical analysis can get richer information, and has a very good application prospect in controlling project cost [8-11].

Project construction management refers to the management carried out in the whole process from the project start preparation to completion and acceptance. Since the real estate development project building construction and installation tasks are usually entrusted to contracted to building construction units to complete, the engineering construction management of development projects [12-15], mainly to contract management as a means, the use of planning, organizing, coordinating, controlling, checking, acceptance, and other methods, the investment objectives, progress goals, quality goals for effective control of development The technical and economic activities in the construction of the project [16-19], in accordance with national standards, norms and contractual objectives, to carry out strict supervision, control and management, in order to ensure the ultimate realization of the overall objectives of the development project [20-21].

Based on BIM technology, research engineering BIM integration model, empowering engineering digital transformation and upgrading, has become the top priority of engineering informatization needs. For the engineering information model is difficult to fully play the role of its data and information problems, this paper is based on the construction of engineering BIM integration model to develop the secondary development of software interfaces for numerical computation, model generalization and mesh dissecting technology and other means, to build a dynamic construction simulation method based on BIM technology. Secondly, for the contact problem existing in the project, the form based on the nearest point mapping is used, and the classical Coulomb friction model is adopted for the simulation of the tangential surface force on the contact surface, and the augmented Lagrangian multiplier method is used to deal with the constraints on the contact surface. After that, the numerical simulation results are applied to practical engineering applications and compared and analyzed with the monitoring data.

2

Construction and optimization of engineering BIM integration model

2.1

Modeling

The integrated engineering BIM model consists of engineering structural body and 3D geologic body model, and the differences between structural body and geologic body models in the expression form are deeply considered in the integrated integrated modeling. As for the computational grid generation part of the numerical analysis, the two types of models show a large difference in the degree of geometric regularity, the engineering structure model from parametric modeling shows a more regular geometry, with obvious geometric features, and its geometric features can be described with simpler information; while the 3D geologic body constructed by 3D geologic modeling fails to show regular geometric features, and its geometric features can not be described with simple information. The 3D geoid constructed by 3D geologic modeling fails to show regular geometric features and cannot be described by simple information. To address this difference, mesh delineation techniques for engineering structural models and mesh delineation techniques for integrated models were developed considering both structural models with and without geometrical topology processing of geologic bodies.

The engineering BIM integrated model necessitates the extraction and output of material properties. The material parameters are extracted in the order of the structural material parameters in the structural material parameter list in the first material number, and the elastic modulus, Poisson’s ratio, and bulk weight of the concrete material are mainly obtained. At the same time as the structure output, the boundary conditions and load information on each structural body are also acquired synchronously. The boundary conditions and load information are matched according to the number of the structure output, and are applied one by one to the corresponding structure when outputting to the APDL format file, thus completing the process of constraining and applying loads.

Once all the structural positional information, geometric information, material property information, boundary condition, and loading information are acquired, the process of outputting is carried out. ANSYS APDL format file can completely cover the whole process of ANSYS from modeling to calculation, including the following parts: clearing the previous calculation and analysis information, geometric parameters and material properties, geometric modeling process, assigning material properties to structural units and unit types, bonding all structural bodies together through Boolean operations and mesh delineation, completing the pre-processing to enter the solver and then defining the Analysis type, constraints and loads are defined to solve and complete the finite element analysis.

Engineering structural body BIM model conversion interface calculation example analysis: In order to better verify the effectiveness of the above interface program in practical engineering applications, this section combines a project for analysis. This paper establishes a BIM model of the project through Revit, analyzes the force situation of the structure under the action of foundation bottom constraints and self-weight loads, and the structural part of the model can be displayed through the visibility graphic adjustment.

The interface program is loaded by running the .dll application extension and then run in Revit, selecting structural elements such as beams, slabs, columns, and foundations according to the program’s filtering functions. After the interface program is run, an APDL file is generated in the specified path. Finally, the APDL file is run in ANSYS, during which ANSYS will follow the command flow instructions to complete the definition of material properties and geometric parameters, structural modeling, constraints and loads, and finally perform calculations and other steps.

After ANSYS completes the above operation process, the total displacement cloud and stress intensity cloud of the model are derived.

2.2

Dynamic scenario optimization method based on integrated models

After simultaneously realizing the step-by-step numerical analysis function and the dynamic construction simulation function of the BIM integrated model, considering the service demand of the actual project, the scheme optimization method based on the integrated model is developed by combining the numerical analysis and dynamic construction. For the part of engineering structure, using the BIM model conversion interface, real-time output BIM model to finite element model conversion, and numerical calculation analysis; furthermore, according to the monitoring data during the specific construction of the actual project, with the results of numerical calculations, with reference to the design standards, the information in the monitoring and calculations is fed back to the BIM model, which assists in the optimization of the engineering structure BIM model for the design of the scheme. For the part of the BIM integrated model, the mesh mapping and common surface constraints are used to cope with the complex and irregular geological body model, the mesh division of the BIM integrated model is carried out, and at the same time, the simulation parameters and working conditions of the integrated simulation model are set up, so as to carry out step-by-step numerical calculation and analysis.

Further, the numerical calculation results are fed back to the various stages of construction simulation to provide numerical support for construction plan selection and building structure optimization, which guides the actual construction process of the project, and the complete dynamic construction plan optimization method is shown in Figure 1.

3

Mechanical mechanism and optimization method of contact surface unit

3.1

Types of contact surface units

In general, contact surface units can be broadly categorized into three types: two-node units, Goodman units, and thin-layer units. Among them, the latter two types are more widely studied. 1)

Two-node unit

On each side of the contact surface at the same position, there is a node, and these two nodes form a cell. The unit consists of normal and tangential springs with coefficients of strength of k_n and k_s, respectively.

When the contact surface is cracked, k_s and k_n are taken as very small values to reflect the contact surface on both sides of the force-free connection; if the contact surface is not cracked, k_n is taken as a very large value. If the shear stress reaches the destructive shear stress t_f, k_s takes a very small value, otherwise it takes a large value.

2)

Goodman unit

Assuming that there is no cross-influence between normal stress and shear stress on the contact surface and normal relative displacement and tangential relative displacement, the relationship between stress and relative displacement is equation (1): (1) ${\begin{array}{l} σ_{n} \\ τ \end{array}} = [\begin{matrix} k_{n} & 0 \\ 0 & k_{s} \end{matrix}] {\begin{array}{l} ω_{n} \\ ω_{s} \end{array}}$

where ω_s, ω_n are tangential and normal relative displacements of the contact surface; k_s, k_n are tangential and normal coefficients of strength, respectively. Where k_s is determined according to the straight shear experiment. The value of k_n is the same as that of the two-node unit. 3)

Thin-layer unit

In order to avoid no thickness unit may cause the two sides of the unit overlap each other, as well as simulate the contact surface shear damage often occurs in the vicinity of the soil body this phenomenon, many Chinese and foreign scholars advocate the use of a thickness of the thin layer unit. Assuming that the thickness of the unit is t, the contact surface stress ~ strain relationship can be expressed as equation (2): (2) ${\begin{array}{l} σ_{n} \\ τ \end{array}} = [\begin{matrix} t k_{n n} & t k_{n s} \\ t k_{s n} & t k_{s s} \end{matrix}] {\begin{array}{l} ε_{n} \\ γ \end{array}}$

where k_nn is the normal stiffness coefficient; k_ss is the tangential stiffness coefficient; k_ns, k_sn are the coupling coefficients between tangential and normal directions.

3.2

Mechanical mechanisms and optimization methods for contact units

3.2.1

Coulomb Friction Modeling

The Coulomb friction model is derived from the friction model for rigid bodies. The Coulomb friction model is given when applied to each point on the contact interface:

If A and B are in contact at X, then we have equations (3) and (4) (3) $‖ t_{T} ‖ < - μ \cdot t_{N}, g_{T} = u_{T}^{A} - u_{T}^{B} = 0$ (4) $‖ t_{T} ‖ = - μ \cdot t_{N}, g_{T} = u_{T}^{A} - u_{T}^{B} > 0$

The condition that the two objects are in contact at a point implies a normal force t_N ≤ 0. Therefore, the right-hand term − μ · t_N of both expressions is always positive. Condition a corresponds to sticking, when the tangential surface force at a point is less than a critical value, no tangential relative displacement is allowed, i.e., the two objects are sticking. Condition b corresponds to sliding, and tangential relative displacement g_T occurs when the tangential surface force reaches a critical value.

When applying the Coulomb friction model, care must also be taken to avoid the situation where the boundary shear stress calculated from the Coulomb friction theory exceeds the yield limit of the material when the contact pressure is very high. At this time the contact interface is not sliding, but the material has already yielded, so to avoid this situation, a maximum allowable shear stress τ_max needs to be specified. A reasonable estimate can be taken as $σ_{y} / \sqrt{3}$ (σ_y is the Mises yield stress of the material).

3.2.2

Weak forms of contact interface conditions

For clarity, the frictionless contact interface case is considered first, followed by the treatment of tangential surface forces. The contact surface is neither a force nor a displacement boundary condition. The full boundary of object A is equation (5): (5) $Γ^{A} = Γ_{l}^{A} \cup Γ_{u}^{A} \cup Γ^{c}$

where $Γ_{l}^{A}$ , $Γ_{u}^{A}$ , and Γ^c are the force boundary, displacement boundary, and contact interface, respectively. 1)

Weak form of Lagrange multiplier

The usual method of imposing contact constraints is by means of Lagrange multipliers. Following the description given by Belytschko and Neal, the Lagrange multiplier test function is given as λ(ζ) and the corresponding variational function is given as δλ(ζ). These functions exist in the following spaces (6) and (7): (6) $λ (ζ) \in j^{+}, j^{+} = {λ (ζ) | λ \in C^{- 1}, λ \geq 0 Γ^{c}}$ (7) $δ λ (ζ) \in j^{-}, j^{-} = {δ λ (ζ) | δ λ \in C^{- 1}, δ λ \leq 0 Γ^{c}}$

The weak form is (8): (8) $δ P_{L} (u, δ u, λ, δ λ) \equiv δ p + δ G_{L} \geq 0$

where there are equations (9) and (10) (9) $δ P = \int_{Ω} \frac{\partial (δ u_{i})}{\partial x_{j}} σ_{j i} d Ω - \int_{Ω} δ u_{i} ρ b_{i} d Ω - \int_{Γ_{i}} δ u_{i} \bar{t_{i}} d Γ$ (10) $δ G_{L} = \int_{Γ^{c}} δ (λ g_{N}) d Γ$

Eq. (9) is the weak form of the updated Lagrange format. where the first integral is now the internal virtual work, the second term is the external virtual work arising from the volume force of b_i, and the third term is the external virtual work due to the face force ${\bar{t}}_{i}$ specified on the force boundary Γ_t.

Eq. (8) is an inequality that contains the face force boundary condition, the inviolability condition, and the force equilibrium condition for the contacting normal face force.The Lagrange multiplier field requires only that C⁻¹ be continuous, since its derivative does not appear in the weak form. The requirement that the normal interface force be a pressure is a restriction on the Lagrange multipliers in the trial space. The internal virtual work is obtained by partial integration and application of Gauss’s principle: (11) $\int_{Ω} {(δ u_{i} σ_{j i})}_{j j} d Ω = \int_{Γ_{i}} δ u_{j} σ_{j i} n_{j} d Γ + \int_{Γ^{'}} (δ u_{i}^{A} t_{j}^{d} + δ u_{i}^{B} t_{i}^{B}) d Γ$

Since there is a δu_i = 0 at Γ_u, the integral over the displacement boundary Γ_u is zero, and in the last integral, Cauchy’s law is applied to obtain the expression. The product function of the second integral at the right end of the above equation is decomposed into components perpendicular and tangent to the contact surface: (12) $δ u^{A} \cdot t^{t} = (δ u_{N}^{A} n^{t} + δ u_{T}^{t}) \cdot (t_{N}^{A} n^{A} + t_{T}^{A}) = δ u_{N}^{A} t_{N}^{A} + δ u_{T}^{A} t_{T}^{t}$

Now consider equation (10) with: (13) $δ G_{L} = \int_{Γ^{c}} δ (λ g_{N}) d Γ = \int_{Γ^{c}} (δ λ g_{N} + δ g_{N} λ) d Γ$

Substituting into the above equation, we get (14) $δ G_{L} = \int_{Γ^{C}} (δ λ g_{N} + λ (δ u_{N}^{A} - δ u_{N}^{B})) d Γ$

Substituting equations (11), (12) and (13) into equation (8) yields: (15) $\begin{array}{l} 0 \leq d p_{L} = \int_{Ω} d u_{i} (σ_{j i, j} - ρ b_{i}) d Ω + \int_{Γ_{i}} d u_{i} (σ_{j i} - \bar{t_{i}}) d Γ \\ + \int_{Γ^{c}} [δ u_{N}^{A} (t_{N}^{A} + λ) + δ u_{N}^{B} (t_{N}^{B} - λ) + (δ u_{T}^{t} t_{T}^{A} + δ u_{T}^{B} t_{T}^{B}) + δ λ g_{N}] d Γ \end{array}$

Among all the terms of the contact surface being product function, the variational function is unrestricted except for the last one, and therefore, the following equations (16) and (17) can be obtained: (16) $t_{T}^{A} = t_{T}^{B} = 0 On Γ^{c}$ (17) $λ = - t_{N}^{A} And λ = t_{N}^{B} On Γ^{c}$

Eliminating λ from equation (17) yields the force balance condition (18) for the normal plane force (18) $t_{N}^{t} + t_{N}^{B} = 0 On Γ^{c}$

From Eq. (7), the variational function δλ of the last term of the product function in Eq. (15) I is negative. Therefore, g_N is not necessarily zero, but it can be deduced that g_N is necessarily nonpositive, i.e., the weak inequality representation (19): (19) $g_{N} \leq 0 On Γ^{c}$

Equations (16) to (19) constitute the strong form corresponding to the weak form (8), which includes the conditions for force equilibrium between the two objects, the internal continuity condition and the boundary conditions for the face forces. At the contact surface, the strong form includes the force equilibrium of the normal face forces and the inequality about mutual intrusion. The property that the normal face force is a pressure is derived from the restriction of the Lagrange multiplier variational function, equation (6). 2)

Penalty method

In the penalized method, a non-invasive constraint is applied along the contact surface as a penalized normal face force. In contrast to the Lagrange multiplier method, the penalty method allows for some mutual penetration. However, it is easier to program and is quite widely used. In this paper, the penalty is defined as an arbitrary function of mutual intrusiveness g_N. The weak form is (20): (20) $δ p_{p} (u, δ u) = δ p + δ G_{p} = 0$

which has the formula (21) (21) $δ G_{p} = \int_{Γ^{c}} \frac{β}{2} δ (g_{N}^{2}) H (g_{N}) d Γ$

In the above equation $H (g_{N})$ is the Heaviside distribution function (22) $H (g_{N}) = {\begin{array}{l} 1 & g_{N} > 0 \\ 0 & g_{N} < 0 \end{array}$

The generalized function δp is defined by equation (9); β is the penalty function. The discontinuity nature of the contact problem is introduced by the Heaviside distribution function appearing in Eq. (21). This weak form does not imply an inviolability condition, which is only approximately satisfied in the penalty method.

The above form of the penalty method is often very difficult in arithmetic due to the fact that it may allow for excessive intrusiveness, and the normal surface forces are nonzero only if the relative displacements lead to successive mutual intrusiveness. Once the relative displacements of neighboring points of two surfaces become equal or negative, the normal surface force is zero. Consequently, a certain amount of mutual invagination may exist in the solution. Therefore, in the penalty method, the normal surface force is here made to be also a function of the mutual encroachment. For this purpose, define the interfacial pressure $p = \bar{p} (g_{N}) H (\bar{p})$ in the weak form (23): (23) $δ G_{p} = \int_{Γ^{c}} δ g_{N} p d Γ$

The same process as before gives equation (24) (24) $t_{N}^{A} + p = 0 And t_{N}^{B} - p = 0 on Γ^{c}$

Therefore, the surface force is always a pressure and the force equilibrium condition is satisfied. The penalty function is generally expressed as equation (25): (25) $p = β g_{N}$ 3)

Generalized Lagrangian

The augmented Lagrangian is an improved method of the Lagrange multiplier method. The weak form is: (26) $δ p_{A L} (u, δ u, λ, δ λ) = δ p + δ G_{A L} \geq 0, δ λ \in j^{j}$ (27) $δ G_{A L} = \int_{Γ^{c}} δ [λ g_{N} + \frac{α}{2} g_{N}^{2}] d Γ$

where α serves as the positive parameter to be determined for the distribution solving process. 4)

Tangential surface force with the help of Lagrange multipliers

By attaching an additional term to the weak form that strengthens the continuity of the tangential surface force, the weak forms obtained by the three methods above need to be modified in order to deal with interface friction, such that (28) $δ p_{c} = δ p + δ G_{N} + δ G_{T}$

For Lagrange multiplier methods and augmented Lagrange methods. The weak form is an inequality (29): (29) $δ p_{c} \geq 0 Pawn δ G_{N} = δ G_{L} Or δ G_{A L}$

For the penalty method, the weak form is an equation (30): (30) $δ p_{C} = 0 Pawn δ G_{N} = δ G_{p}$

There is equation (31) in both cases: (31) $δ G_{T} = \int_{Γ^{C}} δ g_{T} \cdot t_{T} d Γ$

where t_T is the surface force tangent to the contact interface, calculated by the friction model.

4

Practical application and analysis of engineering BIM integration modeling

4.1

Project Description and Process

The total length of a drainage network renovation project in Tianjin is about 5km, and the construction process uses both the open excavation and pipe jacking methods. The open excavation section of the proposed site is a construction site, and the pipe jacking section is mostly in the green belt of Donghai Road, and the terrain is generally flat, with the ground elevation ranging from 3.6 to 6.12m.

The working conditions for numerical simulation are consistent with the construction sequence of the site as much as possible. Before excavation calculations, an initial ground stress equilibrium was carried out to simulate the consolidation settlement and stress state of the soil under self-weight. Then the diaphragm wall is constructed (i.e., diaphragm wall units are activated), and historical displacements and velocities are cleared after the calculations are balanced. Finally, excavation analysis is carried out, and the construction process is shown in Table 1.

Table 1.

Numerical simulation condition

Name	Construction process
Initial Equilibrium	Simulate the initial ground stress field of soil under the action of gravity
Working condition 0	Construction of underground diaphragm wall. Velocity, displacement and plastic zones were zeroed out
Working condition 1	Excavation1.0m,to the elevation of 3.82m;Set the first brace
Working condition 2	Excavation6.0m,To elevation -2.78m;Set the second brace
Working condition 3	Excavation5.0m,To elevation -8.1m;Set the third brace

4.2

Deep Horizontal Displacement Results and Analysis

During the construction process, the deep horizontal displacement is shown in Fig. 2, the trend of horizontal displacement is basically the same under each condition, the horizontal displacement along the pile height increases first and then decreases, presenting a “bow-shaped” trend of large in the middle and small at both ends. The maximum horizontal displacement of the enclosure structure is 1.47mm in Case 1, 7.26mm in Case 2, and 16.62mm in Case 3, which is about 0.14% of the excavation depth, and conforms to the safety requirements of the specification.

4.3

Surrounding Surface Settlement Results and Analysis

As the excavation process develops, the amount of surface settlement increases, and the influence range of settlement deformation increases. At the end of excavation, the amount of settlement change reaches its maximum. The surface settlement change curve is shown in Figure 3. Near the edge of the pit, the amount of surface settlement is small, with the increase of the distance from the edge of the pit, the surface settlement first increases and then decreases, and the settlement reaches the maximum at a certain distance from the edge of the pit, and the settlement value tends to 0 at the furthest point, and the maximum surface settlement occurs at the distance from the edge of the pit of 0.5~0.9 times the depth of excavation, respectively. The maximum surface settlement in Case 1 is 0.21mm, and the maximum surface settlement in Case 2 is 0.58mm. At the end of excavation, the maximum surface settlement value is 3.31mm, which is in line with the safety requirements of the specification.

4.4

Comparison and analysis of numerical simulation results with monitoring data

Fig. 4’s (a), (b), and (c) show the comparison curves of the calculated displacements and measured displacements for each working condition, and it can be found that the overall trends of the calculated results and the monitoring results are approximately the same and close in size.

5

Project Cost Optimization Analysis

Numerical simulation technology is applied to the whole project process, and the commercial manager of the project manager department continuously follows up the earned value statistics during the project, and the follow-up statistics values of the three basic parameters are shown in Table 2.

Table 2.

Project construction progress and cost completion

Number of days	Budgeted Cost for Work Scheduled(BCWS)	Budgeted Cost for Work Performed(BCWP)	Actual Cost of Work Performed(ACWP)
18	159.7	159.5	155.3
36	314.4	302.3	296.2
54	800.3	710.3	689.6
72	1456.3	1386.4	1436.2
90	2856.3	2502.9	2723.8
108	5897.5	4263.9	2056.3
126	7897.5	5964.1	6549.7
144	8897.5	79456.3	8265.2
162	10346.4	15275.4	14842.6
180	11946.3	19769	14300.7
198	13931.4	14199.3	15910.6
216	15878.1	16773.2	18882.5
234	17466.4	18705.1	19070.1
252	17999.4	18957.3	19385.3

Meanwhile, based on the values of the three basic parameters in Table 2, the corresponding analyzed parameters were calculated as shown in Table 3.

Table 3.

Project cost and schedule deviation analysis

Number of days	Cost Variance (CV)	Schedule Variance (SV)	Cost Performance Indicator(CPI)	Scheduled Performance Indicator(SPI)
18	3.5	0.6	1.05	1.01
36	9.6	-3.29	1.01	0.88
54	41.8	-52.41	1.03	0.95
72	-57.9	-105.1	1.05	0.81
90	-241.8	-724.21	0.98	0.89
108	-689.3	-390.39	1.05	0.93
126	-957.7	-1155.04	1.02	0.93
144	-831.5	-1160.45	0.87	0.85
162	-323.7	-1081.41	0.94	0.77
180	73.5	-226.76	1.05	1.04
198	20.97	55.3	1.03	1.03
216	290.2	666.9	1.05	1.03
234	423.6	697.2	1.07	1.02
252	513.9	706.3	1.02	1.04

From the calculation results, the CV value is reversed to positive value in the current period from the 180th day, and the SV value is reversed to positive value in the current period from the 198th day.

The positive deviation indexes indicate that the project’s progress and cost are always progressing in a positive direction. From the absolute positive value, the total cost of completion predicted up to the point of time on the 252nd day will be saved by 5,139,000 yuan, with a cost-saving rate of 1.88%, and the absolute positive value of the progress deviation is 7,063,000 yuan, i.e., a progress advancement rate of 3.01%, which means that the construction work will be completed about 13 days ahead of schedule. This indicates that the implementation of the measures has largely met expectations.

6

Conclusion

This paper carries out a systematic research on engineering BIM integration model, for the current engineering BIM integration encountered in the dispersion of information, data model and the actual project can not be highly unified problem, has been used to build a dynamic construction simulation method and broaden the Lagrangian multiplier method to optimize the model. The optimized engineering BIM integration model is theoretically capable of comprehensively simulating and guiding the construction of the actual project in various time periods, directions, and specialties. In the application of the actual project, the simulated numerical results provided by the model and the actual test results have the same overall trend, close to the size, and through the application of numerical simulation technology to achieve cost savings of 5.139 million yuan, the construction period ahead of the 13 days, so that the project’s schedule and cost to the good development. It reflects the effectiveness and superiority of the engineering BIM integration model under the optimization scheme of this paper, which is of great significance to the research of engineering information construction.

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Application of Numerical Simulation Technology in Engineering Management and its Impact on Project Costs

Weiwei Zhang

Publicado en línea: 24 mar 2025

Recibido: 11 oct 2024

Aceptado: 02 feb 2025

DOI: https://doi.org/10.2478/amns-2025-0753

Palabras claveEngineering digitalization, BIM technology, Dynamic construction simulation, Augmented Lagrangian multiplier method, Numerical simulation technology

© 2025 Weiwei Zhang, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Palabras clave
Engineering digitalization, BIM technology, Dynamic construction simulation, Augmented Lagrangian multiplier method, Numerical simulation technology